1
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Panagopoulos H, Vicari E. Out-of-equilibrium scaling of the energy density along the critical relaxational flow after a quench of the temperature. Phys Rev E 2024; 109:064107. [PMID: 39020886 DOI: 10.1103/physreve.109.064107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2024] [Accepted: 05/09/2024] [Indexed: 07/20/2024]
Abstract
We study the out-of-equilibrium behavior of statistical systems along critical relaxational flows arising from instantaneous quenches of the temperature T to the critical point T_{c}, starting from equilibrium conditions at time t=0. In the case of soft quenches, i.e., when the initial temperature T is assumed sufficiently close to T_{c} (to keep the system within the critical regime), the critical modes develop an out-of-equilibrium finite-size-scaling (FSS) behavior in terms of the rescaled time variable Θ=t/L^{z}, where t is the time interval after quenching, L is the size of the system, and z is the dynamic exponent associated with the dynamics. However, the realization of this picture is less clear when considering the energy density, whose equilibrium scaling behavior (corresponding to the starting point of the relaxational flow) is generally dominated by a temperature-dependent regular background term or mixing with the identity operator. These issues are investigated by numerical analyses within the three-dimensional lattice N-vector models, for N=3 and 4, which provide examples of critical behaviors with negative values of the specific-heat critical exponent α, implying that also the critical behavior of the specific heat gets hidden by the background term. The results show that, after subtraction of its asymptotic critical value at T_{c}, the energy density develops an asymptotic out-of-equilibrium FSS in terms of Θ as well, whose scaling function appears singular in the small-Θ limit.
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2
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Ferreira LS, Metz FL. Nonequilibrium dynamics of the Ising model on heterogeneous networks with an arbitrary distribution of threshold noise. Phys Rev E 2023; 107:034127. [PMID: 37073060 DOI: 10.1103/physreve.107.034127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Accepted: 03/03/2023] [Indexed: 04/20/2023]
Abstract
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree distribution in the high-connectivity limit. Depending on the distribution of the threshold noise that governs the microscopic dynamics, the model evolves to nonequilibrium stationary states. We obtain an exact dynamical equation for the distribution of local magnetizations, from which we find the critical line that separates the paramagnetic from the ferromagnetic phase. For random graphs with a negative binomial degree distribution, we demonstrate that the stationary critical behavior as well as the long-time critical dynamics of the first two moments of the local magnetizations depend on the distribution of the threshold noise. In particular, for an algebraic threshold noise, these critical properties are determined by the power-law tails of the distribution of thresholds. We further show that the relaxation time of the average magnetization inside each phase exhibits the standard mean-field critical scaling. The values of all critical exponents considered here are independent of the variance of the negative binomial degree distribution. Our work highlights the importance of certain details of the microscopic dynamics for the critical behavior of nonequilibrium spin systems.
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Affiliation(s)
- Leonardo S Ferreira
- Physics Institute, Federal University of Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| | - Fernando L Metz
- Physics Institute, Federal University of Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
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3
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Marino J, Eckstein M, Foster MS, Rey AM. Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:116001. [PMID: 36075190 DOI: 10.1088/1361-6633/ac906c] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Accepted: 09/08/2022] [Indexed: 06/15/2023]
Abstract
We overview the concept of dynamical phase transitions (DPTs) in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal behavior on the two sides of a certain dynamical critical point. DPTs are currently mostly understood as long-lived prethermal phenomena in a regime where inelastic collisions are incapable to thermalize the system. The latter enables the dynamics to substain phases that explicitly break detailed balance and therefore cannot be encompassed by traditional thermodynamics. Our presentation covers both cold atoms as well as condensed matter systems. We revisit a broad plethora of platforms exhibiting pre-thermal DPTs, which become theoretically tractable in a certain limit, such as for a large number of particles, large number of order parameter components, or large spatial dimension. The systems we explore include, among others, quantum magnets with collective interactions,ϕ4quantum field theories, and Fermi-Hubbard models. A section dedicated to experimental explorations of DPTs in condensed matter and AMO systems connects this large variety of theoretical models.
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Affiliation(s)
- Jamir Marino
- Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
| | - Martin Eckstein
- Department of Physics, University of Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Matthew S Foster
- Department of Physics and Astronomy, Rice University, Houston, TX 77005, United States of America
- Rice Center for Quantum Materials, Rice University, Houston, TX 77005, United States of America
| | - Ana Maria Rey
- JILA, National Institute of Standards and Technology, and Department of Physics,University of Colorado, Boulder, CO 80309, United States of America
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, United States of America
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4
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Far-from-equilibrium universality in the two-dimensional Heisenberg model. Proc Natl Acad Sci U S A 2022; 119:e2122599119. [PMID: 35787047 PMCID: PMC9282433 DOI: 10.1073/pnas.2122599119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
We characterize the universal far-from-equilibrium dynamics of the two-dimensional quantum Heisenberg magnet isolated from its environment. For a broad range of initial conditions, we find a long-lived universal prethermal regime characterized by self-similar behavior of spin-spin correlations. We analytically derive the spatial-temporal scaling exponents and find excellent agreement with numerics using phase space methods. The scaling exponents are insensitive to the choice of initial conditions, which include coherent and incoherent spin states with values of total magnetization and energy in a wide range. Compared to previously studied self-similar dynamics in nonequilibrium O(n) field theories and Bose gases, we find qualitatively distinct scaling behavior originating from the presence of spin modes that remain gapless at long times and are protected by the global SU(2) symmetry. Our predictions, which suggest a distinct nonequilibrium universality class from Bose gases and O(n) theories, are readily testable in ultracold atoms simulators of Heisenberg magnets.
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5
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Halimeh JC, Maghrebi MF. Quantum aging and dynamical universality in the long-range O(N→∞) model. Phys Rev E 2021; 103:052142. [PMID: 34134217 DOI: 10.1103/physreve.103.052142] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2020] [Accepted: 04/29/2021] [Indexed: 11/07/2022]
Abstract
Quantum quenches to or near criticality give rise to the phenomenon of aging, manifested by glassylike dynamics at short times and far from equilibrium. The recent surge of interest in the dynamics of quantum many-body systems has rejuvenated interest in this phenomenon. Motivated by the ubiquitous long-range interactions in emerging experimental platforms, it is vital to study quantum aging in such settings. In this paper, we investigate the dynamical universality and aging in the d-dimensional O(N) model with the long-range coupling 1/x^{d+σ} and in the mean-field limit N→∞ that allows an exact treatment. An immediate consequence of long-range coupling is the emergence of nonlinear light cones. We focus on the correlation and response functions, and identify a rich scaling behavior depending on how the corresponding space-time positions are located relative to each other, via a local light cone, and to the time of the quench via a global quench light cone. We determine the initial-slip exponent that governs the short-time dependence of two-point functions. We highlight the qualitative features of aging due to the long-range coupling, in particular in the region outside the light cones. As an important consequence of long-range coupling, the correlation function decays as 1/x^{d+σ} outside the quench light cone while increasing polynomially with the total time after quench. This is while, for short-time differences, the two-time response function "equilibrates" at all distances even outside this light cone. Our analytic findings are in excellent agreement with exact numerics, and provide a useful benchmark for modern experimental platforms with long-range interactions.
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Affiliation(s)
- Jad C Halimeh
- INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy.,Kirchhoff Institute for Physics, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany.,Institute for Theoretical Physics, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
| | - Mohammad F Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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6
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Pietraszewicz J, Seweryn A, Witkowska E. Multifaceted phase ordering kinetics of an antiferromagnetic spin-1 condensate. Sci Rep 2021; 11:9296. [PMID: 33927249 PMCID: PMC8085072 DOI: 10.1038/s41598-021-88454-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2020] [Accepted: 04/07/2021] [Indexed: 11/18/2022] Open
Abstract
We study phase domain coarsening in the long time limit after a quench of magnetic field in a quasi one-dimensional spin-1 antiferromagnetic condensate. We observe that the growth of correlation length obeys scaling laws predicted by the two different models of phase ordering kinetics, namely the binary mixture and vector field. We derive regimes of clear realization for both of them. We demonstrate appearance of atypical scaling laws, which emerge in intermediate regions.
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Affiliation(s)
- Joanna Pietraszewicz
- Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02668, Warsaw, Poland
| | - Aleksandra Seweryn
- Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02668, Warsaw, Poland
| | - Emilia Witkowska
- Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02668, Warsaw, Poland.
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7
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Bhattacharyya S, Rodriguez-Nieva JF, Demler E. Universal Prethermal Dynamics in Heisenberg Ferromagnets. PHYSICAL REVIEW LETTERS 2020; 125:230601. [PMID: 33337214 DOI: 10.1103/physrevlett.125.230601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2019] [Accepted: 10/21/2020] [Indexed: 06/12/2023]
Abstract
We study the far from equilibrium prethermal dynamics of magnons in Heisenberg ferromagnets. We show that such systems exhibit universal self-similar scaling in momentum and time of the quasiparticle distribution function, with the scaling exponents independent of microscopic details or initial conditions. We argue that the SU(2) symmetry of the Hamiltonian, which leads to a strong momentum-dependent magnon-magnon scattering amplitude, gives rise to qualitatively distinct prethermal dynamics from that recently observed in Bose gases. We compute the scaling exponents using the Boltzmann kinetic equation and incoherent initial conditions that can be realized with microwave pumping of magnons. We also compare our numerical results with analytic estimates of the scaling exponents and demonstrate the robustness of the scaling to variations in the initial conditions. Our predictions can be tested in quench experiments of spin systems in optical lattices and pump-probe experiments in ferromagnetic insulators such as yttrium iron garnet.
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Affiliation(s)
| | | | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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8
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Titum P, Maghrebi MF. Nonequilibrium Criticality in Quench Dynamics of Long-Range Spin Models. PHYSICAL REVIEW LETTERS 2020; 125:040602. [PMID: 32794797 DOI: 10.1103/physrevlett.125.040602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Revised: 06/07/2020] [Accepted: 06/19/2020] [Indexed: 06/11/2023]
Abstract
Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground-state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick model describing the collective interaction of N spins and investigate the dynamical properties of fluctuations and correlations after a sudden quench of the Hamiltonian. Specifically, we focus on critical quenches, where the initial state and/or the postquench Hamiltonian are critical. Depending on the type of quench, we identify three distinct behaviors where both the short-time dynamics and the stationary state at long times are effectively thermal, quantum, and genuinely nonequilibrium, characterized by distinct universality classes and static and dynamical critical exponents. These behaviors can be identified by an infrared effective temperature that is finite, zero, and infinite (the latter scaling with the system size as N^{1/3}), respectively. The quench dynamics is studied through a combination of exact numerics and analytical calculations utilizing the nonequilibrium Keldysh field theory. Our results are amenable to realization in experiments with trapped-ion experiments where long-range interactions naturally arise.
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Affiliation(s)
- Paraj Titum
- Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland 20723, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Mohammad F Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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9
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Hasenbusch M. Dynamic critical exponent z of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model. Phys Rev E 2020; 101:022126. [PMID: 32168572 DOI: 10.1103/physreve.101.022126] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2019] [Accepted: 02/05/2020] [Indexed: 11/07/2022]
Abstract
We study purely dissipative relaxational dynamics in the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size scaling analysis of the integrated autocorrelation time of the magnetic susceptibility in equilibrium at the critical point. We obtain z=2.0245(15) for the dynamic critical exponent. As a complement, fully magnetized configurations are suddenly quenched to the critical temperature, giving consistent results for the dynamic critical exponent. Furthermore, our estimate of z is fully consistent with recent field theoretic results.
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Affiliation(s)
- Martin Hasenbusch
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany
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10
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Jian SK, Yin S, Swingle B. Universal Prethermal Dynamics in Gross-Neveu-Yukawa Criticality. PHYSICAL REVIEW LETTERS 2019; 123:170606. [PMID: 31702242 DOI: 10.1103/physrevlett.123.170606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Indexed: 06/10/2023]
Abstract
We study the prethermal dynamics of the Gross-Neveu-Yukawa quantum field theory, suddenly quenched in the vicinity of a critical point. We find that the universal prethermal dynamics is controlled by two fixed points depending on the size of the quench. Besides the usual equilibrium chiral Ising fixed point for a shallow quench, a dynamical chiral Ising fixed point is identified for a deep quench. Intriguingly, the latter is a nonthermal fixed point without any equilibrium counterpart due to the participation of gapless fermionic fields. We also find that in the scaling regime controlled by the equilibrium fixed point, the initial slip exponent is rendered negative if there are enough flavors of fermions, thus providing a unique signature of fermionic prethermal dynamics. We then explore the temporal crossover between the universal scaling regimes governed by the two universality classes. Possible experimental realizations are also discussed.
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Affiliation(s)
- Shao-Kai Jian
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Shuai Yin
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- School of physics, Sun Yat-Sen University, Guangzhou 510275, China
| | - Brian Swingle
- Condensed Matter Theory Center, Maryland Center for Fundamental Physics, Joint Center for Quantum Information and Computer Science, and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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11
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Gross M, Rohwer CM, Dietrich S. Dynamics of the critical Casimir force for a conserved order parameter after a critical quench. Phys Rev E 2019; 100:012114. [PMID: 31499903 DOI: 10.1103/physreve.100.012114] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2019] [Indexed: 06/10/2023]
Abstract
Fluctuation-induced forces occur generically when long-range correlations (e.g., in fluids) are confined by external bodies. In classical systems, such correlations require specific conditions, e.g., a medium close to a critical point. On the other hand, long-range correlations appear more commonly in certain nonequilibrium systems with conservation laws. Consequently, a variety of nonequilibrium fluctuation phenomena, including fluctuation-induced forces, have been discovered and explored recently. Here we address a long-standing problem of nonequilibrium critical Casimir forces emerging after a quench to the critical point in a confined fluid with order-parameter-conserving dynamics and non-symmetry-breaking boundary conditions. The interplay of inherent (critical) fluctuations and dynamical nonlocal effects (due to density conservation) gives rise to striking features, including correlation functions and forces exhibiting oscillatory time dependences. Complex transient regimes arise, depending on initial conditions and the geometry of the confinement. Our findings pave the way for exploring a wealth of nonequilibrium processes in critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In certain regimes, our results are applicable to active matter.
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Affiliation(s)
- Markus Gross
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Christian M Rohwer
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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12
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Piñeiro Orioli A, Berges J. Breaking the Fluctuation-Dissipation Relation by Universal Transport Processes. PHYSICAL REVIEW LETTERS 2019; 122:150401. [PMID: 31050509 DOI: 10.1103/physrevlett.122.150401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2018] [Indexed: 06/09/2023]
Abstract
Universal phenomena far from equilibrium exhibit additional independent scaling exponents and functions as compared to thermal universal behavior. For the example of an ultracold Bose gas we simulate nonequilibrium transport processes in a universal scaling regime and show how they lead to the breaking of the fluctuation-dissipation relation. As a consequence, the scaling of spectral functions (commutators) and statistical correlations (anticommutators) between different points in time and space become linearly independent with distinct dynamic scaling exponents. As a macroscopic signature of this phenomenon, we identify a transport peak in the statistical two-point correlator, which is absent in the spectral function showing the quasiparticle peaks of the Bose gas.
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Affiliation(s)
- Asier Piñeiro Orioli
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Jürgen Berges
- Institute for Theoretical Physics, Heidelberg University, Philosophenweg 16, 69120 Heidelberg, Germany
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13
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Corberi F, Kumar M, Lippiello E, Puri S. Effects of frustration on fluctuation-dissipation relations. Phys Rev E 2019; 99:012131. [PMID: 30780308 DOI: 10.1103/physreve.99.012131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2018] [Indexed: 06/09/2023]
Abstract
We study numerically the aging properties of the two-dimensional Ising model with quenched disorder considered in our recent paper [Phys. Rev. E 95, 062136 (2017)2470-004510.1103/PhysRevE.95.062136], where frustration can be tuned by varying the fraction of antiferromagnetic interactions. Specifically, we focus on the scaling properties of the autocorrelation and linear response functions after a quench of the model to a low temperature. We find that the interplay between equilibrium and aging occurs differently in the various regions of the phase diagram of the model. When the quench is made into the ferromagnetic phase the two-time quantities are made by the sum of an equilibrium and an aging part, whereas in the paramagnetic phase these parts combine in a multiplicative way. Scaling forms are shown to be obeyed with good accuracy, and the corresponding exponents and scaling functions are determined and discussed in the framework of what is known in clean and disordered systems.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Fisica "E. R. Caianiello", and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
| | - Manoj Kumar
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Eugenio Lippiello
- Department of Mathematics and Physics, University of Campania "L. Vanvitelli", Viale Lincoln 5, 81100 Caserta, Italy
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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14
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Erne S, Bücker R, Gasenzer T, Berges J, Schmiedmayer J. Universal dynamics in an isolated one-dimensional Bose gas far from equilibrium. Nature 2018; 563:225-229. [PMID: 30405227 DOI: 10.1038/s41586-018-0667-0] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2018] [Accepted: 09/28/2018] [Indexed: 11/09/2022]
Abstract
Understanding the behaviour of isolated quantum systems far from equilibrium and their equilibration is one of the most pressing problems in quantum many-body physics1,2. There is strong theoretical evidence that sufficiently far from equilibrium a wide variety of systems-including the early Universe after inflation3-6, quark-gluon matter generated in heavy-ion collisions7-9, and cold quantum gases4,10-14-exhibit universal scaling in time and space during their evolution, independent of their initial state or microscale properties. However, direct experimental evidence is lacking. Here we demonstrate universal scaling in the time-evolving momentum distribution of an isolated, far-from-equilibrium, one-dimensional Bose gas, which emerges from a three-dimensional ultracold Bose gas by means of a strong cooling quench. Within the scaling regime, the time evolution of the system at low momenta is described by a time-independent, universal function and a single scaling exponent. The non-equilibrium scaling describes the transport of an emergent conserved quantity towards low momenta, which eventually leads to the build-up of a quasi-condensate. Our results establish universal scaling dynamics in an isolated quantum many-body system, which is a crucial step towards characterizing time evolution far from equilibrium in terms of universality classes. Universality would open the possibility of using, for example, cold-atom set-ups at the lowest energies to simulate important aspects of the dynamics of currently inaccessible systems at the highest energies, such as those encountered in the inflationary early Universe.
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Affiliation(s)
- Sebastian Erne
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Vienna, Austria.,Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany.,School of Mathematical Sciences, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, UK
| | - Robert Bücker
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Vienna, Austria.,Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Thomas Gasenzer
- Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany.,Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
| | - Jürgen Berges
- Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
| | - Jörg Schmiedmayer
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Vienna, Austria.
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15
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Lerose A, Marino J, Žunkovič B, Gambassi A, Silva A. Chaotic Dynamical Ferromagnetic Phase Induced by Nonequilibrium Quantum Fluctuations. PHYSICAL REVIEW LETTERS 2018; 120:130603. [PMID: 29694194 DOI: 10.1103/physrevlett.120.130603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Revised: 12/22/2017] [Indexed: 06/08/2023]
Abstract
We investigate the robustness of a dynamical phase transition against quantum fluctuations by studying the impact of a ferromagnetic nearest-neighbor spin interaction in one spatial dimension on the nonequilibrium dynamical phase diagram of the fully connected quantum Ising model. In particular, we focus on the transient dynamics after a quantum quench and study the prethermal state via a combination of analytic time-dependent spin wave theory and numerical methods based on matrix product states. We find that, upon increasing the strength of the quantum fluctuations, the dynamical critical point fans out into a chaotic dynamical phase within which the asymptotic ordering is characterized by strong sensitivity to the parameters and initial conditions. We argue that such a phenomenon is general, as it arises from the impact of quantum fluctuations on the mean-field out of equilibrium dynamics of any system which exhibits a broken discrete symmetry.
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Affiliation(s)
- Alessio Lerose
- SISSA-International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
- INFN-Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34136 Trieste, Italy
| | - Jamir Marino
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
| | - Bojan Žunkovič
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
- INFN-Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34136 Trieste, Italy
| | - Alessandro Silva
- SISSA-International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
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16
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Pelissetto A, Vicari E. Dynamic finite-size scaling at first-order transitions. Phys Rev E 2018; 96:012125. [PMID: 29347172 DOI: 10.1103/physreve.96.012125] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2017] [Indexed: 11/07/2022]
Abstract
We investigate the dynamic behavior of finite-size systems close to a first-order transition (FOT). We develop a dynamic finite-size scaling (DFSS) theory for the dynamic behavior in the coexistence region where different phases coexist. This is characterized by an exponentially large time scale related to the tunneling between the two phases. We show that, when considering time scales of the order of the tunneling time, the dynamic behavior can be described by a two-state coarse-grained dynamics. This allows us to obtain exact predictions for the dynamical scaling functions. To test the general DFSS theory at FOTs, we consider the two-dimensional Ising model in the low-temperature phase, where the external magnetic field drives a FOT, and the 20-state Potts model, which undergoes a thermal FOT. Numerical results for a purely relaxational dynamics fully confirm the general theory.
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Affiliation(s)
- Andrea Pelissetto
- Dipartimento di Fisica dell'Università di Roma "La Sapienza" and INFN, Sezione di Roma I, I-00185 Rome, Italy
| | - Ettore Vicari
- Dipartimento di Fisica dell'Università di Pisa and INFN, Sezione di Pisa, I-56127 Pisa, Italy
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17
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Muñoz-Gil G, Charalambous C, García-March MA, Garcia-Parajo MF, Manzo C, Lewenstein M, Celi A. Transient subdiffusion from an Ising environment. Phys Rev E 2018; 96:052140. [PMID: 29347809 DOI: 10.1103/physreve.96.052140] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2017] [Indexed: 11/07/2022]
Abstract
We introduce a model in which a particle performs a continuous-time random walk (CTRW) coupled to an environment with Ising dynamics. The particle shows locally varying diffusivity determined by the geometrical properties of the underlying Ising environment, that is, the diffusivity depends on the size of the connected area of spins pointing in the same direction. The model shows anomalous diffusion when the Ising environment is at critical temperature. We show that any finite scale introduced by a temperature different from the critical one, or a finite size of the environment, cause subdiffusion only during a transient time. The characteristic time, at which the system returns to normal diffusion after the subdiffusive plateau depends on the limiting scale and on how close the temperature is to criticality. The system also displays apparent ergodicity breaking at intermediate time, while ergodicity breaking at longer time occurs only under the idealized infinite environment at the critical temperature.
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Affiliation(s)
- G Muñoz-Gil
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - C Charalambous
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - M A García-March
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - M F Garcia-Parajo
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.,ICREA-Pg. Lluís Companys 23, 08010 Barcelona, Spain
| | - C Manzo
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.,Universitat de Vic-Universitat Central de Catalunya (UVic-UCC), C. de la Laura, 13, 08500 Vic, Spain
| | - M Lewenstein
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.,ICREA-Pg. Lluís Companys 23, 08010 Barcelona, Spain
| | - A Celi
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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18
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Meyer H, Voigtmann T, Schilling T. On the non-stationary generalized Langevin equation. J Chem Phys 2017; 147:214110. [DOI: 10.1063/1.5006980] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Hugues Meyer
- Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
- Research Unit in Engineering Science, Université du Luxembourg, L-4364 Esch-sur-Alzette, Luxembourg
| | - Thomas Voigtmann
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany
- Department of Physics, Heinrich Heine University, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Tanja Schilling
- Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
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19
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Karl M, Cakir H, Halimeh JC, Oberthaler MK, Kastner M, Gasenzer T. Universal equilibrium scaling functions at short times after a quench. Phys Rev E 2017; 96:022110. [PMID: 28950605 DOI: 10.1103/physreve.96.022110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2017] [Indexed: 06/07/2023]
Abstract
By analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.
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Affiliation(s)
- Markus Karl
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Halil Cakir
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Jad C Halimeh
- Physics Department and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Markus K Oberthaler
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Michael Kastner
- National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa
- Department of Physics, Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch 7600, South Africa
| | - Thomas Gasenzer
- Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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20
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Foini L, Gambassi A, Konik R, Cugliandolo LF. Measuring effective temperatures in a generalized Gibbs ensemble. Phys Rev E 2017; 95:052116. [PMID: 28618551 DOI: 10.1103/physreve.95.052116] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Indexed: 06/07/2023]
Abstract
The local physical properties of an isolated quantum statistical system in the stationary state reached long after a quench are generically described by the Gibbs ensemble, which involves only its Hamiltonian and the temperature as a parameter. If the system is instead integrable, additional quantities conserved by the dynamics intervene in the description of the stationary state. The resulting generalized Gibbs ensemble involves a number of temperature-like parameters, the determination of which is practically difficult. Here we argue that in a number of simple models these parameters can be effectively determined by using fluctuation-dissipation relationships between response and correlation functions of natural observables, quantities which are accessible in experiments.
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Affiliation(s)
- Laura Foini
- Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland
- Laboratoire de Physique Statistique, Département de l'ENS, École Normale Supérieure, PSL Research University, Université Paris Diderot, Sorbonne Paris Cité, Sorbonne Universités, UPMC Univ. Paris 06, CNRS, 75005 Paris, France
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy
| | - Robert Konik
- CMPMS Division, Brookhaven National Laboratory, Building 734, Upton, New York 11973, USA
| | - Leticia F Cugliandolo
- Sorbonne Universités, Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique et Hautes Energies, 4, Place Jussieu, Tour 13, 5ème étage, 75252 Paris Cedex 05, France
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21
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Chiocchetta A, Gambassi A, Diehl S, Marino J. Dynamical Crossovers in Prethermal Critical States. PHYSICAL REVIEW LETTERS 2017; 118:135701. [PMID: 28409986 DOI: 10.1103/physrevlett.118.135701] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2016] [Indexed: 06/07/2023]
Abstract
We study the prethermal dynamics of an interacting quantum field theory with an N-component order parameter and O(N) symmetry, suddenly quenched in the vicinity of a dynamical critical point. Depending on the initial conditions, the evolution of the order parameter, and of the response and correlation functions, can exhibit a temporal crossover between universal dynamical scaling regimes governed, respectively, by a quantum and a classical prethermal fixed point, as well as a crossover from a Gaussian to a non-Gaussian prethermal dynamical scaling. Together with a recent experiment, this suggests that quenches may be used in order to explore the rich variety of dynamical critical points occurring in the nonequilibrium dynamics of a quantum many-body system. We illustrate this fact by using a combination of renormalization group techniques and a nonperturbative large-N limit.
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Affiliation(s)
- Alessio Chiocchetta
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
| | - Sebastian Diehl
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
| | - Jamir Marino
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
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22
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Pelissetto A, Vicari E. Dynamic Off-Equilibrium Transition in Systems Slowly Driven across Thermal First-Order Phase Transitions. PHYSICAL REVIEW LETTERS 2017; 118:030602. [PMID: 28157338 DOI: 10.1103/physrevlett.118.030602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2016] [Indexed: 06/06/2023]
Abstract
We study the off-equilibrium behavior of systems with short-range interactions, slowly driven across a thermal first-order transition, where the equilibrium dynamics is exponentially slow. We consider a dynamics that starts in the high-T phase at time t=t_{i}<0 and ends at t=t_{f}>0 in the low-T phase, with a time-dependent temperature T(t)/T_{c}≈1-t/t_{s}, where t_{s} is the protocol time scale. A general off-equilibrium scaling (OS) behavior emerges in the limit of large t_{s}. We check it at the first-order transition of the two-dimensional q-state Potts model with q=20 and 10. The numerical results show evidence of a dynamic transition, where the OS functions show a spinodal-like singularity. Therefore, the general mean-field picture valid for systems with long-range interactions is qualitatively recovered, provided the time dependence is appropriately (logarithmically) rescaled.
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Affiliation(s)
- Andrea Pelissetto
- Dipartimento di Fisica di Sapienza, Università di Roma and INFN, Sezione di Roma I, I-00185 Roma, Italy
| | - Ettore Vicari
- Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
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23
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Duclut C, Delamotte B. Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark. Phys Rev E 2017; 95:012107. [PMID: 28208463 DOI: 10.1103/physreve.95.012107] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2016] [Indexed: 06/06/2023]
Abstract
We derive the necessary conditions for implementing a regulator that depends on both momentum and frequency in the nonperturbative renormalization-group flow equations of out-of-equilibrium statistical systems. We consider model A as a benchmark and compute its dynamical critical exponent z. This allows us to show that frequency regulators compatible with causality and the fluctuation-dissipation theorem can be devised. We show that when the principle of minimal sensitivity (PMS) is employed to optimize the critical exponents η, ν, and z, the use of frequency regulators becomes necessary to make the PMS a self-consistent criterion.
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Affiliation(s)
- Charlie Duclut
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Bertrand Delamotte
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 place Jussieu, 75252 Paris Cedex 05, France
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24
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Lulli M, Parisi G, Pelissetto A. Out-of-equilibrium finite-size method for critical behavior analyses. Phys Rev E 2016; 93:032126. [PMID: 27078311 DOI: 10.1103/physreve.93.032126] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2015] [Indexed: 06/05/2023]
Abstract
We present a dynamic off-equilibrium method for the study of continuous transitions, which represents a dynamic generalization of the usual equilibrium cumulant method. Its main advantage is that critical parameters are derived from numerical data obtained much before equilibrium has been attained. Therefore, the method is particularly useful for systems with long equilibration times, like spin glasses. We apply it to the three-dimensional Ising spin-glass model, obtaining accurate estimates of the critical exponents and of the critical temperature with a limited computational effort.
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Affiliation(s)
- Matteo Lulli
- Physics of Fluids Group, University of Twente, 7500AE Enschede, The Netherlands
- Department of Applied Physics, Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Netherlands
| | - Giorgio Parisi
- Dipartimento di Fisica di "Sapienza", Università di Roma, I-00185 Roma, Italy
- INFN, Sezione di Roma I, I-00185 Roma, Italy
| | - Andrea Pelissetto
- Dipartimento di Fisica di "Sapienza", Università di Roma, I-00185 Roma, Italy
- INFN, Sezione di Roma I, I-00185 Roma, Italy
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25
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Pelissetto A, Vicari E. Off-equilibrium scaling behaviors driven by time-dependent external fields in three-dimensional O(N) vector models. Phys Rev E 2016; 93:032141. [PMID: 27078326 DOI: 10.1103/physreve.93.032141] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2015] [Indexed: 06/05/2023]
Abstract
We consider the dynamical off-equilibrium behavior of the three-dimensional O(N) vector model in the presence of a slowly varying time-dependent spatially uniform magnetic field H(t)=h(t)e, where e is an N-dimensional constant unit vector, h(t)=t/t(s), and t(s) is a time scale, at fixed temperature T≤T(c), where T(c) corresponds to the continuous order-disorder transition. The dynamic evolutions start from equilibrium configurations at h(i)<0, correspondingly t(i)<0, and end at time t(f)>0 with h(t(f))>0, or vice versa. We show that the magnetization displays an off-equilibrium scaling behavior close to the transition line H(t)=0. It arises from the interplay among the time t, the time scale t(s), and the finite size L. The scaling behavior can be parametrized in terms of the scaling variables t(s)(κ)/L and t/t(s)(κ(t)), where κ>0 and κ(t)>0 are appropriate universal exponents, which differ at the critical point and for T<T(c). In the latter case, κ and κ(t) also depend on the shape of the lattice and on the boundary conditions. We present numerical results for the Heisenberg (N=3) model under a purely relaxational dynamics. They confirm the predicted off-equilibrium scaling behaviors at and below T(c). We also discuss hysteresis phenomena in round-trip protocols for the time dependence of the external field. We define a scaling function for the hysteresis loop area of the magnetization that can be used to quantify how far the system is from equilibrium.
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Affiliation(s)
- Andrea Pelissetto
- Dipartimento di Fisica dell'Università di Roma "La Sapienza" and INFN, Sezione di Roma I, I-00185 Roma, Italy
| | - Ettore Vicari
- Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
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26
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Maghrebi MF, Gorshkov AV. Nonequilibrium many-body steady states via Keldysh formalism. PHYSICAL REVIEW. B 2016; 93:10.1103/PhysRevB.93.014307. [PMID: 31093593 PMCID: PMC6513009 DOI: 10.1103/physrevb.93.014307] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under nonequilibrium dynamics. While these states and their phase transitions have been studied extensively with mean-field theory, the validity of the mean-field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean-field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class.
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Affiliation(s)
- Mohammad F. Maghrebi
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V. Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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27
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Tartaglia A, Cugliandolo LF, Picco M. Percolation and coarsening in the bidimensional voter model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042109. [PMID: 26565170 DOI: 10.1103/physreve.92.042109] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2015] [Indexed: 06/05/2023]
Abstract
We study the bidimensional voter model on a square lattice with numerical simulations. We demonstrate that the evolution takes place in two distinct dynamic regimes; a first approach towards critical site percolation and a further approach towards full consensus. We calculate the time dependence of the two growing lengths, finding that they are both algebraic but with different exponents (apart from possible logarithmic corrections). We analyze the morphology and statistics of clusters of voters with the same opinion. We compare these results to the ones for curvature driven two-dimensional coarsening.
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Affiliation(s)
- Alessandro Tartaglia
- Sorbonne Universités, Université Pierre et Marie Curie-Paris VI, Laboratoire de Physique Théorique et Hautes Energies UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Leticia F Cugliandolo
- Sorbonne Universités, Université Pierre et Marie Curie-Paris VI, Laboratoire de Physique Théorique et Hautes Energies UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Marco Picco
- Sorbonne Universités, Université Pierre et Marie Curie-Paris VI, Laboratoire de Physique Théorique et Hautes Energies UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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28
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Maraga A, Chiocchetta A, Mitra A, Gambassi A. Aging and coarsening in isolated quantum systems after a quench: Exact results for the quantum O(N) model with N → ∞. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042151. [PMID: 26565212 DOI: 10.1103/physreve.92.042151] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2015] [Indexed: 06/05/2023]
Abstract
The nonequilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.
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Affiliation(s)
- Anna Maraga
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
| | - Alessio Chiocchetta
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
| | - Aditi Mitra
- Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, I-34136 Trieste, Italy
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29
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Riesch C, Radons G, Magerle R. Aging of orientation fluctuations in stripe phases. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052101. [PMID: 25493734 DOI: 10.1103/physreve.90.052101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2014] [Indexed: 06/04/2023]
Abstract
Stripe patterns, observed in a large variety of physical systems, often exhibit a slow nonequilibrium dynamics because ordering is impeded by the presence of topological defects. Using computer simulations based on a well-established model for stripe formation, we show that a slow dynamics and aging occur also in stripe patterns free of topological defects. For a wide range of noise strengths, the two-time orientation correlation function follows a scaling form that is typical for systems exhibiting a growing length scale. In our case, the underlying mechanism is the coarsening of orientation fluctuations, ultimately leading to power-law spatial correlations perpendicular to the stripes. Our results show that even for the smallest amount of noise, stripe phases without topological defects do not reach equilibrium. This constitutes an important aspect of the dynamics of modulated phases.
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Affiliation(s)
- Christian Riesch
- Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
| | - Günter Radons
- Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
| | - Robert Magerle
- Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
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30
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Shimer MT, Täuber UC, Pleimling M. Nonequilibrium relaxation and aging scaling of the Coulomb and Bose glass. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032111. [PMID: 25314399 DOI: 10.1103/physreve.90.032111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2014] [Indexed: 06/04/2023]
Abstract
We employ Monte Carlo simulations to investigate the nonequilibrium relaxation properties of the two- and three-dimensional Coulomb glass with different long-range repulsive interactions. Specifically, we explore the aging scaling laws in the two-time density autocorrelation function. We find that, in the time window and parameter range accessible to us, the scaling exponents are not universal, depending on the filling fraction and temperature: As either the temperature decreases or the filling fraction deviates more from half filling, the exponents reflect markedly slower relaxation kinetics. In comparison with a repulsive Coulomb potential, appropriate for impurity states in strongly disordered semiconductors, we observe that, for logarithmic interactions, the soft pseudogap in the density of states is considerably broader, and the dependence of the scaling exponents on external parameters is much weaker. The latter situation is relevant for flux creep in the disorder-dominated Bose glass phase of type-II superconductors subject to columnar pinning centers.
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Affiliation(s)
- Matthew T Shimer
- Department of Physics (MC 0435), Robeson Hall, 850 West Campus Drive, Virginia Tech, Blacksburg, Virginia 24061, USA and hMetrix LLC, 150 Monument Rd, # 107, Bala Cynwyd, Pennsylvania 19004, USA
| | - Uwe C Täuber
- Department of Physics (MC 0435), Robeson Hall, 850 West Campus Drive, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Michel Pleimling
- Department of Physics (MC 0435), Robeson Hall, 850 West Campus Drive, Virginia Tech, Blacksburg, Virginia 24061, USA
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31
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Zhou NJ, Zheng B, Dai JH. Dynamic approach to finite-temperature magnetic phase transitions in the extended J1-J2 model with vacancy order. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022113. [PMID: 23496466 DOI: 10.1103/physreve.87.022113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2012] [Revised: 01/14/2013] [Indexed: 06/01/2023]
Abstract
The recently discovered iron-based superconductors A(y)Fe(2-x)Se(2) (A=K, Rb, Cs, Tl) show a long-range antiferromagnetic order with an unexpectedly high transition temperature T(N)~550 K and a unique √5×√5 vacancy order. Taking the extended J(1)-J(2) model as a minimal model, we investigate the finite-temperature magnetic phase transitions in a square lattice with a √5×√5 vacancy superstructure by using large-scale Monte Carlo simulations. By the parallel tempering technique, the block spin checkerboard and stripe antiferromagnetic states are detected to be the ground states for three representative sets of model parameters. The short-time dynamic approach is applied to accurately determine the critical temperature as well as the static and dynamic exponents. Our results indicate that the dramatic enhancement of the critical temperature as observed in experiments should be mainly due to a combination of the vacancy order and the block lattice contraction.
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Affiliation(s)
- N J Zhou
- Department of Physics, Hangzhou Normal University, Hangzhou 310036, People's Republic of China.
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32
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Afzal N, Pleimling M. Aging processes in systems with anomalous slow dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012114. [PMID: 23410290 DOI: 10.1103/physreve.87.012114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2012] [Indexed: 06/01/2023]
Abstract
Recently, different numerical studies of coarsening in disordered systems have shown the existence of a crossover from an initial, transient, power-law domain growth to a slower, presumably logarithmic, growth. However, due to the very slow dynamics and the long-lasting transient regime, one is usually not able to fully enter the asymptotic regime when investigating the relaxation of these systems toward equilibrium. We here study two simple driven systems-the one-dimensional ABC model and a related domain model with simplified dynamics-that are known to exhibit anomalous slow relaxation where the asymptotic logarithmic growth regime is readily accessible. Studying two-times correlation and response functions, we focus on aging processes and dynamical scaling during logarithmic growth. Using the time-dependent growth length as the scaling variable, a simple aging picture emerges that is expected to also prevail in the asymptotic regime of disordered ferromagnets and spin glasses.
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Affiliation(s)
- Nasrin Afzal
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA
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33
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Mitra A. Time evolution and dynamical phase transitions at a critical time in a system of one-dimensional bosons after a quantum quench. PHYSICAL REVIEW LETTERS 2012; 109:260601. [PMID: 23368544 DOI: 10.1103/physrevlett.109.260601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2012] [Revised: 09/30/2012] [Indexed: 06/01/2023]
Abstract
A renormalization group approach is used to show that a one-dimensional system of bosons subject to a lattice quench exhibits a finite-time dynamical phase transition where an order parameter within a light cone increases as a nonanalytic function of time after a critical time. Such a transition is also found for a simultaneous lattice and interaction quench where the effective scaling dimension of the lattice becomes time dependent, crucially affecting the time evolution of the system. Explicit results are presented for the time evolution of the boson interaction parameter and the order parameter for the dynamical transition as well as for more general quenches.
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Affiliation(s)
- Aditi Mitra
- Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA
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Gross M, Varnik F. Simulation of static critical phenomena in nonideal fluids with the lattice Boltzmann method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:056707. [PMID: 23004903 DOI: 10.1103/physreve.85.056707] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2011] [Indexed: 06/01/2023]
Abstract
A fluctuating nonideal fluid at its critical point is simulated with the lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A finite-size scaling analysis is applied to determine the critical exponents related to the order parameter, compressibility and specific heat. A particular focus is put on finite-size effects and issues related to the global conservation of the order parameter.
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Affiliation(s)
- M Gross
- Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universität Bochum, Germany.
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Lander B, Seifert U, Speck T. Effective confinement as origin of the equivalence of kinetic temperature and fluctuation-dissipation ratio in a dense shear-driven suspension. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021103. [PMID: 22463149 DOI: 10.1103/physreve.85.021103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2011] [Indexed: 05/31/2023]
Abstract
We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a "hybrid" form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow.
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Affiliation(s)
- Boris Lander
- II. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, DE-70550 Stuttgart, Germany
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Collura M. Off-equilibrium relaxational dynamics with an improved Ising Hamiltonian. JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT 2010; 2010:P12036. [DOI: 10.1088/1742-5468/2010/12/p12036] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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37
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Zhou NJ, Zheng B. Dynamic effect of overhangs and islands at the depinning transition in two-dimensional magnets. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:031139. [PMID: 21230057 DOI: 10.1103/physreve.82.031139] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2010] [Revised: 09/05/2010] [Indexed: 05/30/2023]
Abstract
With the Monte Carlo methods, we systematically investigate the short-time dynamics of domain-wall motion in the two-dimensional random-field Ising model with a driving field (DRFIM). We accurately determine the depinning transition field and critical exponents. Through two different definitions of the domain interface, we examine the dynamics of overhangs and islands. At the depinning transition, the dynamic effect of overhangs and islands reaches maximum. We argue that this should be an important mechanism leading the DRFIM model to a different universality class from the Edwards-Wilkinson equation with quenched disorder.
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Affiliation(s)
- N J Zhou
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
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38
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Biroli G, Cugliandolo LF, Sicilia A. Kibble-Zurek mechanism and infinitely slow annealing through critical points. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:050101. [PMID: 20866169 DOI: 10.1103/physreve.81.050101] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2010] [Indexed: 05/29/2023]
Abstract
We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering systems during an infinitely slow annealing across a second-order phase transition. We elucidate the time and cooling rate dependence of the typical growing length, and we use it to predict the number of topological defects left over in the symmetry broken phase as a function of time, both close and far from the critical region. Our results extend the Kibble-Zurek mechanism and reveal its limitations.
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Affiliation(s)
- Giulio Biroli
- CEA, Institut de Physique Théorique (IPhT) URA 2306, F-91191 Gif-sur-Yvette, France
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39
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Krüger M, Fuchs M. Nonequilibrium fluctuation-dissipation relations of interacting Brownian particles driven by shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:011408. [PMID: 20365374 DOI: 10.1103/physreve.81.011408] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2009] [Indexed: 05/29/2023]
Abstract
We present a detailed analysis of the fluctuation-dissipation theorem (FDT) close to the glass transition in colloidal suspensions under steady shear using mode coupling approximations. Starting point is the many-particle Smoluchowski equation. Under shear, detailed balance is broken and the response functions in the stationary state are smaller at long times than estimated from the equilibrium FDT. An asymptotically constant relation connects response and fluctuations during the shear driven decay, restoring the form of the FDT with, however, a ratio different from the equilibrium one. At short times, the equilibrium FDT holds. We follow two independent approaches whose results are in qualitative agreement. To discuss the derived fluctuation-dissipation ratios, we show an exact reformulation of the susceptibility which contains not the full Smoluchowski operator as in equilibrium, but only its well defined Hermitian part. This Hermitian part can be interpreted as governing the dynamics in the frame comoving with the probability current. We present a simple toy model which illustrates the FDT violation in the sheared colloidal system.
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Affiliation(s)
- Matthias Krüger
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
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40
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Prudnikov VV, Prudnikov PV, Krinitsyn AS, Vakilov AN, Pospelov EA, Rychkov MV. Short-time dynamics and critical behavior of the three-dimensional site-diluted Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:011130. [PMID: 20365346 DOI: 10.1103/physreve.81.011130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2009] [Indexed: 05/29/2023]
Abstract
Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations p=0.95 and 0.8 at criticality. In contrast to studies of the critical behavior of the pure systems by the short-time dynamics method, our investigations of site-diluted Ising model have revealed three stages of the dynamic evolution characterizing a crossover phenomenon from the critical behavior typical for the pure systems to behavior determined by the influence of disorder. The static and dynamic critical exponents are determined with the use of the corrections to scaling for systems starting separately from ordered and disordered initial states. The obtained values of the exponents demonstrate a universal behavior of weakly site-diluted Ising model in the critical region. The values of the exponents are compared to results of numerical simulations which have been obtained in various works and, also, with results of the renormalization-group description of this model.
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Kolton AB, Schehr G, Le Doussal P. Universal nonstationary dynamics at the depinning transition. PHYSICAL REVIEW LETTERS 2009; 103:160602. [PMID: 19905684 DOI: 10.1103/physrevlett.103.160602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2009] [Revised: 09/04/2009] [Indexed: 05/28/2023]
Abstract
We study the nonstationary dynamics of an elastic interface in a disordered medium at the depinning transition. We compute the two-time response and correlation functions, found to be universal and characterized by two independent critical exponents. We find a good agreement between two-loop functional renormalization group calculations and molecular dynamics simulations for the scaling forms, and for the response aging exponent theta_{R}. We also describe a dynamical dimensional crossover, observed at long times in the relaxation of a finite system. Our results are relevant for the nonsteady driven dynamics of domain walls in ferromagnetic films and contact lines in wetting.
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42
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Dudka M, Folk R, Moser G. Dynamic scaling functions and amplitude ratios of stochastic models with energy conservation above Tc. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:031124. [PMID: 19905079 DOI: 10.1103/physreve.80.031124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2009] [Revised: 06/15/2009] [Indexed: 05/28/2023]
Abstract
Dynamical scaling functions above Tc for the characteristic frequencies and the dynamical correlation functions of the order parameter and the conserved density of model C are calculated in one loop order. By a proper exponentiation procedure these results can be extended in order to consider the changes in these functions using the fixed point values and exponents in two loop order. The dynamical amplitude ratio R of the characteristic frequencies is generalized to the critical region. Surprisingly the decay of the shape functions at large scaled frequency does not behave as expected from applying scaling arguments. The exponent upsilon of the decay does not change when going from the critical to the hydrodynamic region although the shape functions change. The value of upsilon for the order parameter is in agreement with its value in the critical region, whereas for the conserved density it is equal to 2, the value in the hydrodynamic region.
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Affiliation(s)
- M Dudka
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, UA-79011 Lviv, Ukraine
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43
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Gomez-Solano JR, Petrosyan A, Ciliberto S, Chetrite R, Gawedzki K. Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a nonequilibrium steady state. PHYSICAL REVIEW LETTERS 2009; 103:040601. [PMID: 19659337 DOI: 10.1103/physrevlett.103.040601] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2009] [Indexed: 05/28/2023]
Abstract
A modified fluctuation-dissipation theorem for a nonequilibrium steady state is experimentally checked by studying the position fluctuations of a colloidal particle whose motion is confined in a toroidal optical trap. The nonequilibrium steady state is generated by means of a rotating laser beam which exerts on the particle a sinusoidal conservative force plus a constant nonconservative one. The modified fluctuation-dissipation theorem is perfectly verified by the experimental data. It can be interpreted as an equilibriumlike fluctuation-dissipation relation in the Lagrangian frame of the mean local velocity of the particle.
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Affiliation(s)
- J R Gomez-Solano
- Université de Lyon, Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, 69364 Lyon CEDEX 07, France
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44
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Patanè D, Silva A, Sols F, Amico L. Thermalization dynamics close to a quantum phase transition. PHYSICAL REVIEW LETTERS 2009; 102:245701. [PMID: 19659029 DOI: 10.1103/physrevlett.102.245701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2008] [Indexed: 05/28/2023]
Abstract
We investigate the dissipative dynamics of a quantum critical system in contact with a thermal bath, focusing on the response of the system to a sudden change of the bath temperature, in analogy to studies of aging. The specific example of the XY model in a transverse magnetic field whose spins are locally coupled to a set of bosonic baths is considered. We analyze the spin-spin correlations and block correlations and identify some universal features in the out-of-equilibrium dynamics. Two distinct regimes, characterized by different time and length scales, emerge. The initial transient dynamics is characterized by the same critical exponents as those of the equilibrium quantum phase transition and resembles the dynamics of thermal phase transitions. At long times equilibrium is reached through the propagation along the chain of a thermal front in a manner similar to the classical Glauber dynamics.
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Affiliation(s)
- Dario Patanè
- MATIS CNR-INFM & Dipartimento di Metodologie Fisiche e Chimiche (DMFCI), Università di Catania, I - 95125 Catania, Italy
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45
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Dong RH, Zheng B, Zhou NJ. Critical domain-wall dynamics of model B. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:051125. [PMID: 19518434 DOI: 10.1103/physreve.79.051125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2009] [Indexed: 05/27/2023]
Abstract
With Monte Carlo methods, we simulate the critical domain-wall dynamics of model B, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, a dynamic scaling form is revealed. Due to the existence of the quasirandom walkers, the magnetization shows intrinsic dependence on the lattice size L . An exponent which governs the L dependence of the magnetization is measured to be sigma=0.243(8) .
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Affiliation(s)
- R H Dong
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
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46
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Head DA. Critical scaling and aging in cooling systems near the jamming transition. PHYSICAL REVIEW LETTERS 2009; 102:138001. [PMID: 19392404 DOI: 10.1103/physrevlett.102.138001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2008] [Indexed: 05/27/2023]
Abstract
We conduct athermal simulations of freely cooling, viscous soft spheres around the jamming transition density varphi(J) and find evidence for a growing length xi(t) that governs relaxation to mechanical equilibrium. xi(t) is manifest in both the velocity correlation function and the spatial correlations in a scalar measure of local force balance which we define. Data for different densities varphi can be collapsed onto two master curves by scaling xi(t) and t by powers of |varphi-varphi(J)|, indicative of critical scaling. Furthermore, particle transport for varphi>varphi(J) exhibits aging and superdiffusion similar to a range of soft matter experiments, suggesting a common origin. Finally, we explain how xi(t) at late times maps onto known behavior away from varphi(J).
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Affiliation(s)
- David A Head
- Institute of Industrial Science, University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan
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47
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He YY, Zheng B, Zhou NJ. Logarithmic correction to scaling in domain-wall dynamics at Kosterlitz-Thouless phase transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:021107. [PMID: 19391706 DOI: 10.1103/physreve.79.021107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2008] [Indexed: 05/27/2023]
Abstract
With Monte Carlo simulations, we investigate the relaxation dynamics of domain walls at the Kosterlitz-Thouless phase transition, taking the two-dimensional XY model as an example. The dynamic scaling behavior is carefully analyzed, and a domain-wall roughening process is observed. Two-time correlation functions are calculated and aging phenomena are investigated. Inside the domain interface, a strong logarithmic correction to scaling is detected.
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Affiliation(s)
- Y Y He
- Zhejiang University, Zhejiang Institute of Modern Physics, Hangzhou 310027, People's Republic of China
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48
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Lin SZ, Zheng B. Short-time critical dynamics at perfect and imperfect surfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:011127. [PMID: 18763939 DOI: 10.1103/physreve.78.011127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2008] [Indexed: 05/26/2023]
Abstract
With Monte Carlo simulations, we study the dynamic relaxation at perfect and imperfect surfaces of the three-dimensional Ising model with an ordered initial state. The time evolution of the surface magnetization, the line magnetization of the defect line, and the corresponding susceptibilities and second cumulants is carefully examined. Universal dynamic scaling forms including a dynamic crossover scaling form are identified at the ordinary, special, and surface phase transitions. The critical exponents beta1 of the surface magnetization and beta2 of the line magnetization are extracted. The impact of the defect line on the universality classes is investigated.
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Affiliation(s)
- S Z Lin
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, China
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49
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Elgart V, Pleimling M. Aging processes in reversible reaction-diffusion systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051134. [PMID: 18643053 DOI: 10.1103/physreve.77.051134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2008] [Indexed: 05/26/2023]
Abstract
Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with reversible reactions. Starting from the exact Langevin equations describing these models, we derive expressions for two-time correlation and autoresponse functions and obtain a simple aging behavior for these quantities. The autoresponse function is thereby found to depend on the specific nature of the chosen perturbation of the system.
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Affiliation(s)
- Vlad Elgart
- Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435, USA
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50
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Zhou NJ, Zheng B. Nonequilibrium critical dynamics with domain wall and surface. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051104. [PMID: 18643023 DOI: 10.1103/physreve.77.051104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2008] [Indexed: 05/26/2023]
Abstract
With Monte Carlo simulations, we investigate the relaxation dynamics with a domain wall for magnetic systems at the critical temperature. The dynamic scaling behavior is carefully analyzed, and a dynamic roughening process is observed. For comparison, similar analysis is applied to the relaxation dynamics with a free or disordered surface.
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Affiliation(s)
- N J Zhou
- Zhejiang University, Zhejiang Institute of Modern Physics, Hangzhou 310027, People's Republic of China
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