1
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Scher Y, Kumar A, Santhanam MS, Reuveni S. Continuous gated first-passage processes. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:108101. [PMID: 39208840 DOI: 10.1088/1361-6633/ad7530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2024] [Accepted: 08/29/2024] [Indexed: 09/04/2024]
Abstract
Gated first-passage processes, where completion depends on both hitting a target and satisfying additional constraints, are prevalent across various fields. Despite their significance, analytical solutions to basic problems remain unknown, e.g. the detection time of a diffusing particle by a gated interval, disk, or sphere. In this paper, we elucidate the challenges posed by continuous gated first-passage processes and present a renewal framework to overcome them. This framework offers a unified approach for a wide range of problems, including those with single-point, half-line, and interval targets. The latter have so far evaded exact solutions. Our analysis reveals that solutions to gated problems can be obtained directly from the ungated dynamics. This, in turn, reveals universal properties and asymptotic behaviors, shedding light on cryptic intermediate-time regimes and refining the notion of high-crypticity for continuous-space gated processes. Moreover, we extend our formalism to higher dimensions, showcasing its versatility and applicability. Overall, this work provides valuable insights into the dynamics of continuous gated first-passage processes and offers analytical tools for studying them across diverse domains.
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Affiliation(s)
- Yuval Scher
- School of Chemistry, Center for the Physics & Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular & Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
| | - Aanjaneya Kumar
- Department of Physics, Indian Institute of Science Education and Research, Dr Homi Bhabha Road, Pune 411008, India
| | - M S Santhanam
- Department of Physics, Indian Institute of Science Education and Research, Dr Homi Bhabha Road, Pune 411008, India
| | - Shlomi Reuveni
- School of Chemistry, Center for the Physics & Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular & Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
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2
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Radice M. First-passage functionals of Brownian motion in logarithmic potentials and heterogeneous diffusion. Phys Rev E 2023; 108:044151. [PMID: 37978608 DOI: 10.1103/physreve.108.044151] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Accepted: 10/11/2023] [Indexed: 11/19/2023]
Abstract
We study the statistics of random functionals Z=∫_{0}^{T}[x(t)]^{γ-2}dt, where x(t) is the trajectory of a one-dimensional Brownian motion with diffusion constant D under the effect of a logarithmic potential V(x)=V_{0}ln(x). The trajectory starts from a point x_{0} inside an interval entirely contained in the positive real axis, and the motion is evolved up to the first-exit time T from the interval. We compute explicitly the PDF of Z for γ=0, and its Laplace transform for γ≠0, which can be inverted for particular combinations of γ and V_{0}. Then we consider the dynamics in (0,∞) up to the first-passage time to the origin and obtain the exact distribution for γ>0 and V_{0}>-D. By using a mapping between Brownian motion in logarithmic potentials and heterogeneous diffusion, we extend this result to functionals measured over trajectories generated by x[over ̇](t)=sqrt[2D][x(t)]^{θ}η(t), where θ<1 and η(t) is a Gaussian white noise. We also emphasize how the different interpretations that can be given to the Langevin equation affect the results. Our findings are illustrated by numerical simulations, with good agreement between data and theory.
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Affiliation(s)
- Mattia Radice
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
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3
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Giordano S, Cleri F, Blossey R. Infinite ergodicity in generalized geometric Brownian motions with nonlinear drift. Phys Rev E 2023; 107:044111. [PMID: 37198762 DOI: 10.1103/physreve.107.044111] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2022] [Accepted: 03/25/2023] [Indexed: 05/19/2023]
Abstract
Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g., in finance, in physics, and biology. The definition of the process depends crucially on the interpretation of the stochastic integrals which involves the discretization parameter α with 0≤α≤1, giving rise to the well-known special cases α=0 (Itô), α=1/2 (Fisk-Stratonovich), and α=1 (Hänggi-Klimontovich or anti-Itô). In this paper we study the asymptotic limits of the probability distribution functions of geometric Brownian motion and some related generalizations. We establish the conditions for the existence of normalizable asymptotic distributions depending on the discretization parameter α. Using the infinite ergodicity approach, recently applied to stochastic processes with multiplicative noise by E. Barkai and collaborators, we show how meaningful asymptotic results can be formulated in a transparent way.
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Affiliation(s)
- Stefano Giordano
- University of Lille, CNRS, Centrale Lille, Univ. Polytechnique Hauts-de-France, UMR 8520 - IEMN - Institut d'Électronique, de Microélectronique et de Nanotechnologie, F-59000 Lille, France
| | - Fabrizio Cleri
- University of Lille, Institut d'Électronique, de Microélectronique et de Nanotechnologie (IEMN CNRS UMR8520) and Departement de Physique, F-59652 Villeneuve d'Ascq, France
| | - Ralf Blossey
- University of Lille, Unité de Glycobiologie Structurale et Fonctionnelle (UGSF), CNRS UMR8576, F-59000 Lille, France
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4
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Scher Y, Lauber Bonomo O, Pal A, Reuveni S. Microscopic theory of adsorption kinetics. J Chem Phys 2023; 158:094107. [PMID: 36889971 DOI: 10.1063/5.0121359] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023] Open
Abstract
Adsorption is the accumulation of a solute at an interface that is formed between a solution and an additional gas, liquid, or solid phase. The macroscopic theory of adsorption dates back more than a century and is now well-established. Yet, despite recent advancements, a detailed and self-contained theory of single-particle adsorption is still lacking. Here, we bridge this gap by developing a microscopic theory of adsorption kinetics, from which the macroscopic properties follow directly. One of our central achievements is the derivation of the microscopic version of the seminal Ward-Tordai relation, which connects the surface and subsurface adsorbate concentrations via a universal equation that holds for arbitrary adsorption dynamics. Furthermore, we present a microscopic interpretation of the Ward-Tordai relation that, in turn, allows us to generalize it to arbitrary dimension, geometry, and initial conditions. The power of our approach is showcased on a set of hitherto unsolved adsorption problems to which we present exact analytical solutions. The framework developed herein sheds fresh light on the fundamentals of adsorption kinetics, which opens new research avenues in surface science with applications to artificial and biological sensing and to the design of nano-scale devices.
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Affiliation(s)
- Yuval Scher
- School of Chemistry, Center for the Physics and Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
| | - Ofek Lauber Bonomo
- School of Chemistry, Center for the Physics and Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
| | - Arnab Pal
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
| | - Shlomi Reuveni
- School of Chemistry, Center for the Physics and Chemistry of Living Systems, Ratner Institute for Single Molecule Chemistry, and the Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 6997801 Tel Aviv, Israel
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5
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Liu XP, Yao XC, Li X, Wang YX, Huang CJ, Deng Y, Chen YA, Pan JW. Temperature-Dependent Decay of Quasi-Two-Dimensional Vortices across the BCS-BEC Crossover. PHYSICAL REVIEW LETTERS 2022; 129:163602. [PMID: 36306767 DOI: 10.1103/physrevlett.129.163602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Revised: 08/15/2022] [Accepted: 09/19/2022] [Indexed: 06/16/2023]
Abstract
We systematically study the decay of quasi-two-dimensional vortices in an oblate strongly interacting Fermi gas over a wide interaction range and observe that, as the system temperature is lowered, the vortex lifetime increases in the Bose-Einstein condensate (BEC) regime but decreases at unitarity and in the Bardeen-Cooper-Schrieffer (BCS) regime. The observations can be qualitatively captured by a phenomenological model simply involving diffusion and two-body collisional loss, in which the vortex lifetime is mostly determined by the slower process of the two. In particular, the counterintuitive vortex decay in the BCS regime can be interpreted by considering the competition between the temperature dependence of the vortex annihilation rate and that of unpaired fermions. Our results suggest a competing mechanism for the complex vortex decay dynamics in the BCS-BEC crossover for the fermionic superfluids.
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Affiliation(s)
- Xiang-Pei Liu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Xing-Can Yao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Xiaopeng Li
- State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, and Department of Physics, Fudan University, Shanghai 200433, China
- Shanghai Qi Zhi Institute, AI Tower, Xuhui District, Shanghai 200232, China
| | - Yu-Xuan Wang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chun-Jiong Huang
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Hong Kong, China
| | - Youjin Deng
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
- MinJiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China
| | - Yu-Ao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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6
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Bao JD, Li Y, Marchesoni F. Consistent Hamiltonian models for space-momentum diffusion. Phys Rev E 2022; 105:L052105. [PMID: 35706220 DOI: 10.1103/physreve.105.l052105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Accepted: 05/15/2022] [Indexed: 06/15/2023]
Abstract
We develop a unified Hamiltonian approach to the diffusion of a particle coupled to a dissipative environment, an archetypal model widely invoked to interpret condensed phase phenomena, such as polymerization and cold-atom diffusion in optical lattices. By appropriate choices of the coupling functions, we reformulate phenomenological diffusion models by adding otherwise ignored space-momentum terms. We thus numerically predict a variety of diffusion regimes, from diffusion saturation to superballistic diffusion. With reference to ultracold atoms in optical lattices, we also show that time correlated external noises prevent superdiffusion from exceeding Richardson's law. Some of these results are unexpected and call for experimental validation.
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Affiliation(s)
- Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Yunyun Li
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Fabio Marchesoni
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
- Dipartimento di Fisica, Università di Camerino, I-62032 Camerino, Italy
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7
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Breoni D, Blossey R, Löwen H. Brownian particles driven by spatially periodic noise. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:18. [PMID: 35230521 PMCID: PMC8888531 DOI: 10.1140/epje/s10189-022-00176-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Accepted: 02/18/2022] [Indexed: 05/07/2023]
Abstract
We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can be integrated formally exactly. We determine the short- and long-time behaviour of the mean displacement (MD) and mean-squared displacement (MSD). In particular, we find a very slow dynamics for the mean displacement, scaling as [Formula: see text] with time t. Placed under an additional external periodic force near the critical tilt value we compute the stationary current obtained from the corresponding Fokker-Planck equation and identify an essential singularity if the minimum of the noise strength is zero. Finally, in order to further elucidate the effect of the random periodic driving on the diffusion process, we introduce a phase factor in the spatial noise with respect to the external periodic force and identify the value of the phase shift for which the random force exerts its strongest effect on the long-time drift velocity and diffusion coefficient.
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Affiliation(s)
- Davide Breoni
- Institut für Theoretische Physik II: Weiche Materie, Heinrich, Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany.
| | - Ralf Blossey
- University of Lille, UGSF CNRS UMR8576, 59000, Lille, France
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich, Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
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8
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Rakala G, Damle K, Dhar D. Fractional Brownian motion of worms in worm algorithms for frustrated Ising magnets. Phys Rev E 2021; 103:062101. [PMID: 34271608 DOI: 10.1103/physreve.103.062101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 04/29/2021] [Indexed: 11/07/2022]
Abstract
We study the distribution of lengths and other statistical properties of worms constructed by Monte Carlo worm algorithms in the power-law three-sublattice ordered phase of frustrated triangular and kagome lattice Ising antiferromagnets. Viewing each step of the worm construction as a position increment (step) of a random walker, we demonstrate that the persistence exponent θ and the dynamical exponent z of this random walk depend only on the universal power-law exponents of the underlying critical phase and not on the details of the worm algorithm or the microscopic Hamiltonian. Further, we argue that the detailed balance condition obeyed by such worm algorithms and the power-law correlations of the underlying equilibrium system together give rise to two related properties of this random walk: First, the steps of the walk are expected to be power-law correlated in time. Second, the position distribution of the walker relative to its starting point is given by the equilibrium position distribution of a particle in an attractive logarithmic central potential of strength η_{m}, where η_{m} is the universal power-law exponent of the equilibrium defect-antidefect correlation function of the underlying spin system. We derive a scaling relation, z=(2-η_{m})/(1-θ), that allows us to express the dynamical exponent z(η_{m}) of this process in terms of its persistence exponent θ(η_{m}). Our measurements of z(η_{m}) and θ(η_{m}) are consistent with this relation over a range of values of the universal equilibrium exponent η_{m} and yield subdiffusive (z>2) values of z in the entire range. Thus, we demonstrate that the worms represent a discrete-time realization of a fractional Brownian motion characterized by these properties.
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Affiliation(s)
- Geet Rakala
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0412, Japan
| | - Kedar Damle
- Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400005, India
| | - Deepak Dhar
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
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9
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Liu XP, Yao XC, Deng Y, Wang XQ, Wang YX, Huang CJ, Li X, Chen YA, Pan JW. Universal Dynamical Scaling of Quasi-Two-Dimensional Vortices in a Strongly Interacting Fermionic Superfluid. PHYSICAL REVIEW LETTERS 2021; 126:185302. [PMID: 34018783 DOI: 10.1103/physrevlett.126.185302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2020] [Revised: 09/02/2020] [Accepted: 04/07/2021] [Indexed: 06/12/2023]
Abstract
Vortices play a leading role in many fascinating quantum phenomena. Here we generate a large number of vortices by thermally quenching a fermionic superfluid of ^{6}Li atoms in an oblate optical trap and study their annihilation dynamics and spatial distribution. Over a wide interaction range from the attractive to the repulsive side across the Feshbach resonance, these quasi-two-dimensional vortices are observed to follow algebraic scaling laws both in time and space, having exponents consistent with the two-dimensional universality. We further simulate the classical XY model on the square lattice by a Glauber dynamics and find good agreement between the numerical and experimental behaviors. Our work provides a direct demonstration of the universal 2D vortex dynamics.
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Affiliation(s)
- Xiang-Pei Liu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Xing-Can Yao
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Youjin Deng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
- MinJiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China
| | - Xiao-Qiong Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yu-Xuan Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Chun-Jiong Huang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Xiaopeng Li
- State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing,and Department of Physics, Fudan University, Shanghai 200433, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
| | - Yu-Ao Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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10
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Ray S, Reuveni S. Resetting transition is governed by an interplay between thermal and potential energy. J Chem Phys 2021; 154:171103. [PMID: 34241053 DOI: 10.1063/5.0049642] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A dynamical process that takes a random time to complete, e.g., a chemical reaction, may either be accelerated or hindered due to resetting. Tuning system parameters, such as temperature, viscosity, or concentration, can invert the effect of resetting on the mean completion time of the process, which leads to a resetting transition. Although the resetting transition has been recently studied for diffusion in a handful of model potentials, it is yet unknown whether the results follow any universality in terms of well-defined physical parameters. To bridge this gap, we propose a general framework that reveals that the resetting transition is governed by an interplay between the thermal and potential energy. This result is illustrated for different classes of potentials that are used to model a wide variety of stochastic processes with numerous applications.
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Affiliation(s)
- Somrita Ray
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Shlomi Reuveni
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel
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11
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Zamora A, Lad N, Szymanska MH. Vortex Dynamics in a Compact Kardar-Parisi-Zhang System. PHYSICAL REVIEW LETTERS 2020; 125:265701. [PMID: 33449743 DOI: 10.1103/physrevlett.125.265701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 11/23/2020] [Indexed: 06/12/2023]
Abstract
We study the dynamics of vortices in a two-dimensional, nonequilibrium system, described by the compact Kardar-Parisi-Zhang equation, after a sudden quench across the critical region. Our exact numerical solution of the phase-ordering kinetics shows that the unique interplay between nonequilibrium and the variable degree of spatial anisotropy leads to different critical regimes. We provide an analytical expression for the vortex evolution, based on scaling arguments, which is in agreement with the numerical results, and confirms the form of the interaction potential between vortices in this system.
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Affiliation(s)
- A Zamora
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - N Lad
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - M H Szymanska
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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12
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Nie WP, Zhao ZD, Cai SM, Zhou T. Simulating two-phase taxi service process by random walk theory. CHAOS (WOODBURY, N.Y.) 2020; 30:123121. [PMID: 33380044 DOI: 10.1063/5.0021101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Accepted: 11/23/2020] [Indexed: 06/12/2023]
Abstract
City taxi service systems have been empirically studied by a number of data-driven methods. However, their underlying mechanisms are hard to understand because the present mathematical models neglect to explain a (whole) taxi service process that includes a pair of on-load phase and off-load phase. In this paper, by analyzing a large amount of taxi servicing data from a large city in China, we observe that the taxi service process shows different temporal and spatial features according to the on-load phase and off-load phase. Moreover, our correlation analysis results demonstrate the lack of dependence between the on-load phase and the off-load phase. Hence, we introduce two independent random walk models based on the Langevin equation to describe the underlying mechanism and to understand the temporal and spatial features of the taxi service process. Our study attempts to formulate the mathematical framework for simulating the taxi service process and better understanding of its underlying mechanism.
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Affiliation(s)
- Wei-Peng Nie
- CompleX Lab, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Zhi-Dan Zhao
- Complexity Computation Laboratory, Department of Computer Science, School of Engineering, Shantou University, Shantou 515063, China
| | - Shi-Min Cai
- CompleX Lab, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Tao Zhou
- CompleX Lab, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
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13
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Sabhapandit S, Majumdar SN. Freezing Transition in the Barrier Crossing Rate of a Diffusing Particle. PHYSICAL REVIEW LETTERS 2020; 125:200601. [PMID: 33258622 DOI: 10.1103/physrevlett.125.200601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2020] [Revised: 09/21/2020] [Accepted: 10/08/2020] [Indexed: 06/12/2023]
Abstract
We study the decay rate θ(a) that characterizes the late time exponential decay of the first-passage probability density F_{a}(t|0)∼e^{-θ(a)t} of a diffusing particle in a one dimensional confining potential U(x), starting from the origin, to a position located at a>0. For general confining potential U(x) we show that θ(a), a measure of the barrier (located at a) crossing rate, has three distinct behaviors as a function of a, depending on the tail of U(x) as x→-∞. In particular, for potentials behaving as U(x)∼|x| when x→-∞, we show that a novel freezing transition occurs at a critical value a=a_{c}, i.e., θ(a) increases monotonically as a decreases till a_{c}, and for a≤a_{c} it freezes to θ(a)=θ(a_{c}). Our results are established using a general mapping to a quantum problem and by exact solution in three representative cases, supported by numerical simulations. We show that the freezing transition occurs when in the associated quantum problem, the gap between the ground state (bound) and the continuum of scattering states vanishes.
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Affiliation(s)
| | - Satya N Majumdar
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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14
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Ray S, Reuveni S. Diffusion with resetting in a logarithmic potential. J Chem Phys 2020; 152:234110. [DOI: 10.1063/5.0010549] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Somrita Ray
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Shlomi Reuveni
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel
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15
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Radice M, Onofri M, Artuso R, Pozzoli G. Statistics of occupation times and connection to local properties of nonhomogeneous random walks. Phys Rev E 2020; 101:042103. [PMID: 32422811 DOI: 10.1103/physreve.101.042103] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2020] [Accepted: 03/16/2020] [Indexed: 11/07/2022]
Abstract
We consider the statistics of occupation times, the number of visits at the origin, and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these observables can be characterized by a single exponent, that is connected to a local property of the probability density function of the process, viz., the probability of occupying the origin at time t, P(t). We test our results for two different models of lattice random walks with spatially inhomogeneous transition probabilities, one of which of non-Markovian nature, and find good agreement with theory. We also show that the distributions depend only on the occupation probability of the origin by comparing them for the two systems: When P(t) shows the same long-time behavior, each observable follows indeed the same distribution.
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Affiliation(s)
- Mattia Radice
- Dipartimento di Scienza e Alta Tecnologia and Center for Nonlinear and Complex Systems, Università degli studi dell'Insubria, Via Valleggio 11, I-22100 Como, Italy and I.N.F.N. Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy
| | - Manuele Onofri
- Dipartimento di Scienza e Alta Tecnologia and Center for Nonlinear and Complex Systems, Università degli studi dell'Insubria, Via Valleggio 11, I-22100 Como, Italy and I.N.F.N. Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy
| | - Roberto Artuso
- Dipartimento di Scienza e Alta Tecnologia and Center for Nonlinear and Complex Systems, Università degli studi dell'Insubria, Via Valleggio 11, I-22100 Como, Italy and I.N.F.N. Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy
| | - Gaia Pozzoli
- Dipartimento di Scienza e Alta Tecnologia and Center for Nonlinear and Complex Systems, Università degli studi dell'Insubria, Via Valleggio 11, I-22100 Como, Italy and I.N.F.N. Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy
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16
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Leibovich N, Barkai E. Infinite ergodic theory for heterogeneous diffusion processes. Phys Rev E 2019; 99:042138. [PMID: 31108694 DOI: 10.1103/physreve.99.042138] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2018] [Indexed: 06/09/2023]
Abstract
We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as D(x)∼|x-x[over ̃]|^{2-2/α} in the vicinity of a point x[over ̃], where α can be either positive or negative. We find that a nonnormalized state, also called an infinite density, describes statistical properties of the system. For processes under investigation, the time averages of a wide class of observables are obtained using an ensemble average with respect to the nonnormalized density. A Langevin equation which involves multiplicative noise may take different interpretation, Itô, Stratonovich, or Hänggi-Klimontovich, so the existence of an infinite density and the density's shape are both related to the considered interpretation and the structure of D(x).
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Affiliation(s)
- N Leibovich
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | - E Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 5290002, Israel
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17
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Aghion E, Kessler DA, Barkai E. From Non-Normalizable Boltzmann-Gibbs Statistics to Infinite-Ergodic Theory. PHYSICAL REVIEW LETTERS 2019; 122:010601. [PMID: 31012666 DOI: 10.1103/physrevlett.122.010601] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2018] [Revised: 08/30/2018] [Indexed: 06/09/2023]
Abstract
We study a particle immersed in a heat bath, in the presence of an external force which decays at least as rapidly as 1/x, e.g., a particle interacting with a surface through a Lennard-Jones or a logarithmic potential. As time increases, our system approaches a non-normalizable Boltzmann state. We study observables, such as the energy, which are integrable with respect to this asymptotic thermal state, calculating both time and ensemble averages. We derive a useful canonical-like ensemble which is defined out of equilibrium, using a maximum entropy principle, where the constraints are normalization, finite averaged energy, and a mean-squared displacement which increases linearly with time. Our work merges infinite-ergodic theory with Boltzmann-Gibbs statistics, thus extending the scope of the latter while shedding new light on the concept of ergodicity.
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Affiliation(s)
- Erez Aghion
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
- Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - David A Kessler
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Eli Barkai
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
- Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
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18
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Sieberer LM, Altman E. Topological Defects in Anisotropic Driven Open Systems. PHYSICAL REVIEW LETTERS 2018; 121:085704. [PMID: 30192569 DOI: 10.1103/physrevlett.121.085704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2018] [Indexed: 06/08/2023]
Abstract
We study the dynamics and unbinding transition of vortices in the compact anisotropic Kardar-Parisi-Zhang equation. The combination of nonequilibrium conditions and strong spatial anisotropy drastically affects the structure of vortices and amplifies their mutual binding forces, thus stabilizing the ordered phase. We find novel universal critical behavior in the vortex-unbinding crossover in finite-size systems. These results are relevant for a wide variety of physical systems, ranging from strongly coupled light-matter quantum systems to dissipative time crystals.
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Affiliation(s)
- L M Sieberer
- Department of Physics, University of California, Berkeley, California 94720, USA
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
| | - E Altman
- Department of Physics, University of California, Berkeley, California 94720, USA
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19
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Kumar M, Chatterjee S, Paul R, Puri S. Ordering kinetics in the random-bond XY model. Phys Rev E 2018; 96:042127. [PMID: 29347537 DOI: 10.1103/physreve.96.042127] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2017] [Indexed: 11/07/2022]
Abstract
We present a comprehensive Monte Carlo study of domain growth in the random-bond XY model with nonconserved kinetics. The presence of quenched disorder slows down domain growth in d=2,3. In d=2, we observe power-law growth with a disorder-dependent exponent on the time scales of our simulation. In d=3, we see the signature of an asymptotically logarithmic growth regime. The scaling functions for the real-space correlation function are seen to be independent of the disorder. However, the same does not apply for the two-time autocorrelation function, demonstrating the breakdown of superuniversality.
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Affiliation(s)
- M Kumar
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India
| | - S Chatterjee
- Indian Association for the Cultivation of Science, Kolkata-700032, India
| | - R Paul
- Indian Association for the Cultivation of Science, Kolkata-700032, India
| | - S Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India
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20
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di Santo S, Villegas P, Burioni R, Muñoz MA. Simple unified view of branching process statistics: Random walks in balanced logarithmic potentials. Phys Rev E 2017; 95:032115. [PMID: 28415350 DOI: 10.1103/physreve.95.032115] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Indexed: 11/07/2022]
Abstract
We revisit the problem of deriving the mean-field values of avalanche exponents in systems with absorbing states. These are well known to coincide with those of unbiased branching processes. Here we show that for at least four different universality classes (directed percolation, dynamical percolation, the voter model or compact directed percolation class, and the Manna class of stochastic sandpiles) this common result can be obtained by mapping the corresponding Langevin equations describing each of them into a random walker confined to the origin by a logarithmic potential. We report on the emergence of nonuniversal continuously varying exponent values stemming from the presence of small external driving - that might induce avalanche merging - that, to the best of our knowledge, has not been noticed in the past. Many of the other results derived here appear in the literature as independently derived for individual universality classes or for the branching process itself. Still, we believe that a simple and unified perspective as the one presented here can help (1) clarify the overall picture, (2) underline the superuniversality of the behavior as well as the dependence on external driving, and (3) avoid the common existing confusion between unbiased branching processes (equivalent to a random walker in a balanced logarithmic potential) and standard (unconfined) random walkers.
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Affiliation(s)
- Serena di Santo
- Departamento de Electromagnetismo y Física de la Materia e Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain.,Dipartimento di Fisica e Scienza della Terra, Università di Parma, via G.P. Usberti, 7/A, 43124, Parma, Italy.,INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A, 43124, Parma, Italy
| | - Pablo Villegas
- Departamento de Electromagnetismo y Física de la Materia e Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain
| | - Raffaella Burioni
- Dipartimento di Fisica e Scienza della Terra, Università di Parma, via G.P. Usberti, 7/A, 43124, Parma, Italy.,INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A, 43124, Parma, Italy
| | - Miguel A Muñoz
- Departamento de Electromagnetismo y Física de la Materia e Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain
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21
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Leibovich N, Dechant A, Lutz E, Barkai E. Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise. Phys Rev E 2016; 94:052130. [PMID: 27967149 DOI: 10.1103/physreve.94.052130] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2016] [Indexed: 06/06/2023]
Abstract
The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.
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Affiliation(s)
- N Leibovich
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
| | - A Dechant
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - E Lutz
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - E Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
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22
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Kazakevičius R, Ruseckas J. Influence of external potentials on heterogeneous diffusion processes. Phys Rev E 2016; 94:032109. [PMID: 27739692 DOI: 10.1103/physreve.94.032109] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2016] [Indexed: 06/06/2023]
Abstract
In this paper we consider heterogeneous diffusion processes with the power-law dependence of the diffusion coefficient on the position and investigate the influence of external forces on the resulting anomalous diffusion. The heterogeneous diffusion processes can yield subdiffusion as well as superdiffusion, depending on the behavior of the diffusion coefficient. We assume that not only the diffusion coefficient but also the external force has a power-law dependence on the position. We obtain analytic expressions for the transition probability in two cases: when the power-law exponent in the external force is equal to 2η-1, where 2η is the power-law exponent in the dependence of the diffusion coefficient on the position, and when the external force has a linear dependence on the position. We found that the power-law exponent in the dependence of the mean square displacement on time does not depend on the external force; this force changes only the anomalous diffusion coefficient. In addition, the external force having the power-law exponent different from 2η-1 limits the time interval where the anomalous diffusion occurs. We expect that the results obtained in this paper may be relevant for a more complete understanding of anomalous diffusion processes.
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Affiliation(s)
- Rytis Kazakevičius
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10222 Vilnius, Lithuania
| | - Julius Ruseckas
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10222 Vilnius, Lithuania
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23
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Dechant A, Shafier ST, Kessler DA, Barkai E. Heavy-tailed phase-space distributions beyond Boltzmann-Gibbs: Confined laser-cooled atoms in a nonthermal state. Phys Rev E 2016; 94:022151. [PMID: 27627290 DOI: 10.1103/physreve.94.022151] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2016] [Indexed: 06/06/2023]
Abstract
The Boltzmann-Gibbs density, a central result of equilibrium statistical mechanics, relates the energy of a system in contact with a thermal bath to its equilibrium statistics. This relation is lost for nonthermal systems such as cold atoms in optical lattices, where the heat bath is replaced with the laser beams of the lattice. We investigate in detail the stationary phase-space probability for Sisyphus cooling under harmonic confinement. In particular, we elucidate whether the total energy of the system still describes its stationary state statistics. We find that this is true for the center part of the phase-space density for deep lattices, where the Boltzmann-Gibbs density provides an approximate description. The relation between energy and statistics also persists for strong confinement and in the limit of high energies, where the system becomes underdamped. However, the phase-space density now exhibits heavy power-law tails. In all three cases we find expressions for the leading-order phase-space density and corrections which break the equivalence of probability and energy and violate energy equipartition. The nonequilibrium nature of the steady state is corroborated by explicit violations of detailed balance. We complement these analytical results with numerical simulations to map out the intricate structure of the phase-space density.
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Affiliation(s)
- Andreas Dechant
- Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
- Department of Physics #1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Shalom Tzvi Shafier
- Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
| | - David A Kessler
- Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
| | - Eli Barkai
- Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
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24
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Ryabov A, Berestneva E, Holubec V. Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties. J Chem Phys 2015; 143:114117. [PMID: 26395697 DOI: 10.1063/1.4931474] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Artem Ryabov
- Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic
| | - Ekaterina Berestneva
- Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic
| | - Viktor Holubec
- Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic
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25
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Sonnino G, Steinbrecher G. Generalized extensive entropies for studying dynamical systems in highly anisotropic phase spaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062106. [PMID: 25019724 DOI: 10.1103/physreve.89.062106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2013] [Indexed: 06/03/2023]
Abstract
Starting from the geometrical interpretation of the Rényi entropy, we introduce further extensive generalizations and study their properties. In particular, we found the probability distribution function obtained by the MaxEnt principle with generalized entropies. We prove that for a large class of dynamical systems subject to random perturbations, including particle transport in random media, these entropies play the role of Liapunov functionals. Some physical examples, which can be treated by the generalized Rényi entropies, are also illustrated.
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Affiliation(s)
- Giorgio Sonnino
- Université Libre de Bruxelles (ULB), Department of Physics, Bvd du Triomphe, Campus de la Plaine CP 231, 1050 Brussels, Belgium and Royal Military School (RMS), Av. de la Renaissance 30, 1000 Brussels, Belgium
| | - György Steinbrecher
- Association EURATOM-MEdC, University of Craiova, A. I. Cuza 13, 200585 Craiova, Romania
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26
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Dechant A, Lutz E, Kessler DA, Barkai E. Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:051124. [PMID: 23004720 DOI: 10.1103/physreve.85.051124] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2012] [Indexed: 06/01/2023]
Abstract
We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and we support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the superaging behavior.
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Affiliation(s)
- A Dechant
- Department of Physics, University of Augsburg, 86135 Augsburg, Germany
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27
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Dechant A, Lutz E, Kessler DA, Barkai E. Fluctuations of time averages for Langevin dynamics in a binding force field. PHYSICAL REVIEW LETTERS 2011; 107:240603. [PMID: 22242984 DOI: 10.1103/physrevlett.107.240603] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2011] [Revised: 09/22/2011] [Indexed: 05/31/2023]
Abstract
We derive a simple formula for the fluctuations of the time average x(t) around the thermal mean <x>(eq) for overdamped brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, Schulten, and Schulten in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large nonergodic fluctuations and show how they are related to a superaging correlation function.
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Affiliation(s)
- A Dechant
- Department of Physics, University of Augsburg, D-86135 Augsburg, Germany
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28
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Hirschberg O, Mukamel D, Schütz GM. Approach to equilibrium of diffusion in a logarithmic potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041111. [PMID: 22181091 DOI: 10.1103/physreve.84.041111] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2011] [Indexed: 05/31/2023]
Abstract
The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x∼t(1/2)) and a subdiffusive (x∼t(γ) with a given γ<1/2) length scale, respectively, (ii) the overall scaling function is selected by the initial condition, and (iii) depending on the tail of the initial condition, the scaling exponent that characterizes the scaling function is found to exhibit a transition from a continuously varying to a fixed value.
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Affiliation(s)
- Ori Hirschberg
- Department of Physics of Complex Systems, Weizmann Institute of Science, 76100 Rehovot, Israel
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29
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Martin E, Behn U, Germano G. First-passage and first-exit times of a Bessel-like stochastic process. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:051115. [PMID: 21728498 DOI: 10.1103/physreve.83.051115] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2010] [Revised: 02/13/2011] [Indexed: 05/31/2023]
Abstract
We study a stochastic process X(t) which is a particular case of the Rayleigh process and whose square is the Bessel process, with various applications in physics, chemistry, biology, economics, finance, and other fields. The stochastic differential equation is dX(t)=(nD/X(t))dt+√(2D)dW(t), where W(t) is the Wiener process. The drift term can arise from a logarithmic potential or from taking X(t) as the norm of a multidimensional random walk. Due to the singularity of the drift term for X(t)=0, different natures of boundary at the origin arise depending on the real parameter n: entrance, exit, and regular. For each of them we calculate analytically and numerically the probability density functions of first-passage times or first-exit times. Nontrivial behavior is observed in the case of a regular boundary.
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Affiliation(s)
- Edgar Martin
- Fachbereich Chemie und WZMW, Philipps-Universität Marburg, Marburg, Germany.
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30
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Bandyopadhyay M, Gupta S, Segal D. DNA breathing dynamics: analytic results for distribution functions of relevant Brownian functionals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:031905. [PMID: 21517523 DOI: 10.1103/physreve.83.031905] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2010] [Indexed: 05/30/2023]
Abstract
We investigate DNA breathing dynamics by suggesting and examining several Brownian functionals associated with bubble lifetime and reactivity. Bubble dynamics is described as an overdamped random walk in the number of broken base pairs. The walk takes place on the Poland-Scheraga free-energy landscape. We suggest several probability distribution functions that characterize the breathing process, and adopt the recently studied backward Fokker-Planck method and the path decomposition method as elegant and flexible tools for deriving these distributions. In particular, for a bubble of an initial size x₀, we derive analytical expressions for (i) the distribution P(t{f}|x₀) of the first-passage time t{f}, characterizing the bubble lifetime, (ii) the distribution P(A|x₀) of the area A until the first-passage time, providing information about the effective reactivity of the bubble to processes within the DNA, (iii) the distribution P(M) of the maximum bubble size M attained before the first-passage time, and (iv) the joint probability distribution P(M,t{m}) of the maximum bubble size M and the time t{m} of its occurrence before the first-passage time. These distributions are analyzed in the limit of small and large bubble sizes. We supplement our analytical predictions with direct numericalsimulations of the related Langevin equation, and obtain a very good agreement in the appropriate limits. The nontrivial scaling behavior of the various quantities analyzed here can, in principle, be explored experimentally.
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Affiliation(s)
- Malay Bandyopadhyay
- Chemical Physics Theory Group, University of Toronto, 80 Saint George Street, Ontario M5S3H6, Canada
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31
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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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Kim E, Lee SJ, Kim B. Nonequilibrium relaxations within the ground-state manifold in the antiferromagnetic Ising model on a triangular lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:021106. [PMID: 17358312 DOI: 10.1103/physreve.75.021106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2006] [Revised: 11/17/2006] [Indexed: 05/14/2023]
Abstract
We present an extensive Monte Carlo simulation study on the nonequilibrium kinetics of triangular antiferromagnetic Ising model within the ground state ensemble which consists of sectors, each of which is characterized by a unique value of the string density p through a dimer covering method. Building upon our recent work [Phys. Rev. E 68, 066127 (2003)] where we considered the nonequilibrium relaxation observed within the dominant sector with p=2/3, we here focus on the nonequilibrium kinetics within the minor sectors with p<2/3. The initial configurations are chosen as those in which the strings are straight and evenly distributed. In the minor sectors, we observe a characteristic spatial anisotropy in both equilibrium and nonequilibrium spatial correlations. We observe emergence of a critical relaxation region (in the spatial and temporal domain) which grows as p deviates from p=2/3. Spatial anisotropy appears in the equilibrium spatial correlation with the characteristic length scale xi(e,V)(p) diverging with vanishing string density as xi(e,V)(p) approximately p(-2) along the vertical direction, while along the horizontal direction the spatial length scale diverges as xi(e,H) approximately p(-1). Analytic forms for the anisotropic equilibrium correlation functions are given. We also find that the spin autocorrelation function A(t) shows a simple scaling behavior A(t)=A(t/tau(A)(p)), where the time scale tau(A)(p) shows a power-law divergence with vanishing p as tau(A)(p) approximately p(-phi) with phi approximately or equal to 4. These features can be understood in terms of random walk nature of the fluctuations of the strings within the typical separation between neighboring strings.
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Affiliation(s)
- Eunhye Kim
- Department of Physics, Changwon National University, Changwon 641-773, Korea
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Kim E, Kim B, Lee SJ. Nonequilibrium critical dynamics of the triangular antiferromagnetic Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:066127. [PMID: 14754289 DOI: 10.1103/physreve.68.066127] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2003] [Revised: 08/29/2003] [Indexed: 05/24/2023]
Abstract
We investigate the nonequilibrium critical dynamics of antiferromagnetic Ising model on a two-dimensional triangular lattice via dynamic Monte Carlo simulation employing spin-flip kinetics. Macroscopic degeneracy of the ground state originating from geometric frustration fundamentally affects the nonequilibrium dynamics of the system. In particular, the defects and the loose spins (whose flip costs no energy) play key roles in the dynamics. The long-time evolution is characterized by a critical dynamic scaling with a growing length scale xi(t). With random initial configurations, xi(t) exhibits a subdiffusive growth in time, xi(t) approximately t(1/z) with 1/z approximately 0.43, while xi(t) shows a diffusive growth with z=2 for the relaxation within the dominant sector of the ground-state manifold. The nonequilibrium critical dynamics therefore exhibits an interesting initial-state dependence. Persistence and the two-time temporal properties are also discussed.
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Affiliation(s)
- Eunhye Kim
- Department of Physics, Changwon National University, Changwon 641-773, Korea
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Fogedby HC. Damped finite-time singularity driven by noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:051105. [PMID: 14682786 DOI: 10.1103/physreve.68.051105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2003] [Indexed: 05/24/2023]
Abstract
We consider the combined influence of linear damping and noise on a dynamical finite-time singularity model for a single degree of freedom. We find that the noise effectively resolves the finite-time singularity and replaces it by a first-passage-time distribution or absorbing state distribution with a peak at the singularity and a long time tail. The damping introduces a characteristic cross-over time. In the early time regime the probability distribution and first-passage-time distribution show a power law behavior with scaling exponent depending on the ratio of the nonlinear coupling strength to the noise strength. In the late time regime the behavior is controlled by the damping. The study might be of relevance in the context of hydrodynamics on a nanometer scale, in material physics, and in biophysics.
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Affiliation(s)
- Hans C Fogedby
- Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark.
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Zheng B, Ren F, Ren H. Corrections to scaling in two-dimensional dynamic XY and fully frustrated XY models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:046120. [PMID: 14683015 DOI: 10.1103/physreve.68.046120] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2003] [Indexed: 05/24/2023]
Abstract
With large-scale Monte Carlo simulations, we investigate the two-dimensional dynamic XY and fully frustrated XY models. Dynamic relaxation starting from a disordered or an ordered state is carefully analyzed. It is confirmed that there is a logarithmic correction to scaling for a disordered start, but a power-law correction for an ordered start. Rather accurate values of the static exponent eta and the dynamic exponent z are estimated.
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Affiliation(s)
- B Zheng
- Physics Department, Zhejiang University, Hangzhou 310027, People's Republic of China
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Fogedby HC, Poutkaradze V. Power laws and stretched exponentials in a noisy finite-time-singularity model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:021103. [PMID: 12241146 DOI: 10.1103/physreve.66.021103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2002] [Indexed: 05/23/2023]
Abstract
We discuss the influence of white noise on a generic dynamical finite-time-singularity model for a single degree of freedom. We find that the noise effectively resolves the finite-time-singularity and replaces it by a first-passage-time or absorbing state distribution with a peak at the singularity and a long time tail exhibiting power law or stretched exponential behavior. The study might be of relevance in the context of hydrodynamics on a nanometer scale, in material physics, and in biophysics.
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Affiliation(s)
- Hans C Fogedby
- Institute of Physics and Astronomy, University of Aarhus, DK-8000, Aarhus C, Denmark.
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Wong GP, Mair RW, Walsworth RL, Cory DG. Measurement of persistence in 1D diffusion. PHYSICAL REVIEW LETTERS 2001; 86:4156-4159. [PMID: 11328119 DOI: 10.1103/physrevlett.86.4156] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2000] [Indexed: 05/23/2023]
Abstract
Using a novel NMR scheme we observed persistence in 1D gas diffusion. Analytical approximations and numerical simulations have indicated that for an initially random array of spins undergoing diffusion, the probability p(t) that the average spin magnetization in a given region has not changed sign (i.e., "persists") up to time t follows a power law t(-straight theta), where straight theta depends on the dimensionality of the system. Using laser-polarized 129Xe gas, we prepared an initial "quasirandom" 1D array of spin magnetization and then monitored the ensemble's evolution due to diffusion using real-time NMR imaging. Our measurements are consistent with analytical and numerical predictions of straight theta approximately 0.12.
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Affiliation(s)
- G P Wong
- Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA
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Ying HP, Zheng B, Yu Y, Trimper S. Corrections to scaling for the two-dimensional dynamic XY model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:035101. [PMID: 11308695 DOI: 10.1103/physreve.63.035101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2000] [Indexed: 05/23/2023]
Abstract
With large-scale Monte Carlo simulations, we confirm that for the two-dimensional XY model, there is a logarithmic correction to scaling in the dynamic relaxation starting from a completely disordered state, while only an inverse power law correction in the case of starting from an ordered state. The dynamic exponent z is z=2.04(1).
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Affiliation(s)
- H P Ying
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
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Berthier L, Holdsworth PCW, Sellitto M. Nonequilibrium critical dynamics of the two-dimensionalXYmodel. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/9/301] [Citation(s) in RCA: 105] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Anton L. Time-Inhomogeneous Fokker-Planck Equation for Wave Distributions in the Abelian Sandpile Model. PHYSICAL REVIEW LETTERS 2001; 86:67-70. [PMID: 11136095 DOI: 10.1103/physrevlett.86.67] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2000] [Revised: 09/06/2000] [Indexed: 05/23/2023]
Abstract
The time and size distributions of the waves of topplings in the Abelian sandpile model are expressed as the first arrival at the origin distribution for a scale invariant, time-inhomogeneous Fokker-Plank equation. Assuming a linear conjecture for the time inhomogeneity exponent as a function of a loop-erased random walk (LERW) critical exponent, suggested by numerical results, this approach allows one to estimate the lower critical dimension of the model and the exact value of the critical exponent for LERW in three dimensions. The avalanche size distribution in two dimensions is found to be the difference between two closed power laws.
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Affiliation(s)
- L Anton
- Institute for Theoretical Physics, University of Stellenbosch, Private Bag X1, 7602 Matieland, South Africa and and Institute of Atomic Physics, INFLPR, Lab 22, P.O. Box MG-36 R76900, Bucharest, Romania
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