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Gopalakrishnan S, Vasseur R. Anomalous transport from hot quasiparticles in interacting spin chains. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:036502. [PMID: 36645909 DOI: 10.1088/1361-6633/acb36e] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Accepted: 01/16/2023] [Indexed: 06/17/2023]
Abstract
Many experimentally relevant quantum spin chains are approximately integrable, and support long-lived quasiparticle excitations. A canonical example of integrable model of quantum magnetism is the XXZ spin chain, for which energy spreads ballistically, but, surprisingly, spin transport can be diffusive or superdiffusive. We review the transport properties of this model using an intuitive quasiparticle picture that relies on the recently introduced framework of generalized hydrodynamics. We discuss how anomalous linear response properties emerge from hierarchies of quasiparticles both in integrable and near-integrable limits, with an emphasis on the role of hydrodynamic fluctuations. We also comment on recent developments including non-linear response, full-counting statistics and far-from-equilibrium transport. We provide an overview of recent numerical and experimental results on transport in XXZ spin chains.
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Affiliation(s)
- Sarang Gopalakrishnan
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, United States of America
- Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, United States of America
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, MA 01003, United States of America
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Grabsch A, Poncet A, Rizkallah P, Illien P, Bénichou O. Exact closure and solution for spatial correlations in single-file diffusion. SCIENCE ADVANCES 2022; 8:eabm5043. [PMID: 35333581 PMCID: PMC8956262 DOI: 10.1126/sciadv.abm5043] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Accepted: 02/02/2022] [Indexed: 05/29/2023]
Abstract
In single-file transport particles diffuse in narrow channels while not overtaking each other. it is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in one dimension. Despite extensive effort, these remained elusive, because they involve an infinite hierarchy of equations. For the symmetric exclusion process, a paradigmatic model of single-file diffusion, we break the hierarchy to unveil and solve a closed exact equation satisfied by these correlations. Beyond quantifying the correlations, the role of this key equation as a tool for interacting particle systems is further demonstrated by its application to out-of-equilibrium situations, other observables, and other representative single-file systems.
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Affiliation(s)
- Aurélien Grabsch
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
| | - Alexis Poncet
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
- Université Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Pierre Rizkallah
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Olivier Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
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Del Campo A. Universal Statistics of Topological Defects Formed in a Quantum Phase Transition. PHYSICAL REVIEW LETTERS 2018; 121:200601. [PMID: 30500249 DOI: 10.1103/physrevlett.121.200601] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2018] [Revised: 09/18/2018] [Indexed: 06/09/2023]
Abstract
When a quantum phase transition is crossed in finite time, critical slowing down leads to the breakdown of adiabatic dynamics and the formation of topological defects. The average density of defects scales with the quench rate following a universal power law predicted by the Kibble-Zurek mechanism. We analyze the full counting statistics of kinks and report the exact kink number distribution in the transverse-field quantum Ising model. Kink statistics is described by the Poisson binomial distribution with all cumulants exhibiting a universal power law scaling with the quench rate. In the absence of finite-size effects, the distribution approaches a normal one, a feature that is expected to apply broadly in systems described by the Kibble-Zurek mechanism.
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Affiliation(s)
- Adolfo Del Campo
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Pinsolle E, Houle S, Lupien C, Reulet B. Non-Gaussian Current Fluctuations in a Short Diffusive Conductor. PHYSICAL REVIEW LETTERS 2018; 121:027702. [PMID: 30085754 DOI: 10.1103/physrevlett.121.027702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2018] [Indexed: 06/08/2023]
Abstract
We report the measurement of the third moment of current fluctuations in a short metallic wire at low temperature. The data are deduced from the statistics of voltage fluctuations across the conductor using a careful determination of environmental contributions. Our results at low bias agree very well with theoretical predictions for coherent transport with no fitting parameter. By increasing the bias voltage we explore the crossover from elastic to inelastic transport.
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Affiliation(s)
- Edouard Pinsolle
- Institut Quantique, Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - Samuel Houle
- Institut Quantique, Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - Christian Lupien
- Institut Quantique, Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - Bertrand Reulet
- Institut Quantique, Département de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
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Dhar A, Saito K, Roy A. Energy Current Cumulants in One-Dimensional Systems in Equilibrium. PHYSICAL REVIEW LETTERS 2018; 120:220603. [PMID: 29906157 DOI: 10.1103/physrevlett.120.220603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2015] [Revised: 04/03/2018] [Indexed: 06/08/2023]
Abstract
A recent theory based on fluctuating hydrodynamics predicts that one-dimensional interacting systems with particle, momentum, and energy conservation exhibit anomalous transport that falls into two main universality classes. The classification is based on behavior of equilibrium dynamical correlations of the conserved quantities. One class is characterized by sound modes with Kardar-Parisi-Zhang scaling, while the second class has diffusive sound modes. The heat mode follows Lévy statistics, with different exponents for the two classes. Here we consider heat current fluctuations in two specific systems, which are expected to be in the above two universality classes, namely, a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Numerical simulations show completely different system-size dependence of current cumulants in these two systems. We explain this numerical observation using a phenomenological model of Lévy walkers with inputs from fluctuating hydrodynamics. This consistently explains the system-size dependence of heat current fluctuations. For the latter system, we derive the cumulant-generating function from a more microscopic theory, which also gives the same system-size dependence of cumulants.
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Affiliation(s)
- Abhishek Dhar
- International Centre for Theoretical Sciences, TIFR, Shivakote Village, Hesaraghatta Hobli, Bengaluru 560089, India
| | - Keiji Saito
- Department of Physics, Keio University, Yokohama 223-8522, Japan
| | - Anjan Roy
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
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Khalaf E, Ostrovsky PM. Localization Effects on Magnetotransport of a Disordered Weyl Semimetal. PHYSICAL REVIEW LETTERS 2017; 119:106601. [PMID: 28949183 DOI: 10.1103/physrevlett.119.106601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2016] [Indexed: 06/07/2023]
Abstract
We study longitudinal magnetotransport in a disordered Weyl semimetal taking into account localization effects in the vicinity of a Weyl node exactly. In a magnetic field, a single chiral Landau level coexists with a number of conventional nonchiral levels. Disorder scattering mixes these topologically different modes leading to very strong localization effects. We derive the average conductance as well as the full distribution function of transmission probabilities along the field direction. Remarkably, we find that localization of the nonchiral modes is greatly enhanced in a strong magnetic field with the typical localization length scaling as 1/B. Technically, we use the nonlinear sigma-model formalism with a topological term describing the chiral states. The problem is solved exactly by mapping to an equivalent transfer matrix Hamiltonian.
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Affiliation(s)
- E Khalaf
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - P M Ostrovsky
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
- L. D. Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia
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Žnidarič M. Large-deviation statistics of a diffusive quantum spin chain and the additivity principle. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042140. [PMID: 24827225 DOI: 10.1103/physreve.89.042140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2014] [Indexed: 06/03/2023]
Abstract
Using the large-deviation formalism, we study the statistics of current fluctuations in a diffusive nonequilibrium quantum spin chain. The boundary-driven XX chain with dephasing consists of a coherent bulk hopping and a local dissipative dephasing. We analytically calculate the exact expression for the second current moment in a system of any length and then numerically demonstrate that in the thermodynamic limit, higher-order cumulants and the large-deviation function can be calculated using the additivity principle or macroscopic hydrodynamic theory. This shows that the additivity principle can also hold in systems that are not purely stochastic, and can in particular be valid in quantum systems. We also show that in large systems, the current fluctuations are the same as in the classical symmetric simple exclusion process.
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Affiliation(s)
- Marko Žnidarič
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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Meerson B, Sasorov PV. Extreme current fluctuations in lattice gases: beyond nonequilibrium steady states. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:010101. [PMID: 24580151 DOI: 10.1103/physreve.89.010101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2013] [Indexed: 06/03/2023]
Abstract
We use the macroscopic fluctuation theory (MFT) to study large current fluctuations in nonstationary diffusive lattice gases. We identify two universality classes of these fluctuations, which we call elliptic and hyperbolic. They emerge in the limit when the deterministic mass flux is small compared to the mass flux due to the shot noise. The two classes are determined by the sign of compressibility of effective fluid, obtained by mapping the MFT into an inviscid hydrodynamics. An example of the elliptic class is the symmetric simple exclusion process, where, for some initial conditions, we can solve the effective hydrodynamics exactly. This leads to a super-Gaussian extreme current statistics conjectured by Derrida and Gerschenfeld [J. Stat. Phys. 137, 978 (2009)] and yields the optimal path of the system. For models of the hyperbolic class, the deterministic mass flux cannot be neglected, leading to a different extreme current statistics.
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Affiliation(s)
- Baruch Meerson
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Pavel V Sasorov
- Keldysh Institute of Applied Mathematics, Moscow 125047, Russia
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Harbola U, Van den Broeck C, Lindenberg K. Large deviation function and fluctuation theorem for classical particle transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012141. [PMID: 24580206 DOI: 10.1103/physreve.89.012141] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2013] [Indexed: 06/03/2023]
Abstract
We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic long-time regime is reached starting from a special propagating initial condition. We show that the steady-state fluctuation theorem holds provided that the distribution of the particle number decays faster than an exponential, implying analyticity of the generating function and a discrete spectrum for its evolution operator.
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Affiliation(s)
- Upendra Harbola
- Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore, Karnataka 560012, India
| | | | - Katja Lindenberg
- Department of Chemistry and Biochemistry and BioCircuits Institute, University of California, San Diego, La Jolla, California 92093-0340, USA
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Simon SH, Moustakas AL. Crossover from conserving to lossy transport in circular random-matrix ensembles. PHYSICAL REVIEW LETTERS 2006; 96:136805. [PMID: 16712019 DOI: 10.1103/physrevlett.96.136805] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2005] [Indexed: 05/09/2023]
Abstract
In a quantum dot with three leads, the transmission matrix t12 between two of these leads is a truncation of a unitary scattering matrix S, which we treat as random. As the number of channels in the third lead is increased, the constraints from the symmetry of S become less stringent and t12 becomes closer to a matrix of complex Gaussian random numbers with no constraints. We consider the distribution of the singular values of t12, which is related to a number of physical quantities.
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Affiliation(s)
- Steven H Simon
- Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974, USA
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Sukhorukov EV, Bulashenko OM. Quantum-to-classical crossover in full counting statistics. PHYSICAL REVIEW LETTERS 2005; 94:116803. [PMID: 15903880 DOI: 10.1103/physrevlett.94.116803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2004] [Indexed: 05/02/2023]
Abstract
The reduction of quantum scattering leads to the suppression of shot noise. In this Letter, we analyze the crossover from the quantum transport regime with universal shot noise to the classical regime where noise vanishes. By making use of the stochastic path integral approach, we find the statistics of transport and the transmission properties of a chaotic cavity as a function of a system parameter controlling the crossover. We identify three different scenarios of the crossover.
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Affiliation(s)
- Eugene V Sukhorukov
- Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland
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Pilgram S, Samuelsson P. Noise and full counting statistics of incoherent multiple Andreev reflection. PHYSICAL REVIEW LETTERS 2005; 94:086806. [PMID: 15783919 DOI: 10.1103/physrevlett.94.086806] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2004] [Indexed: 05/24/2023]
Abstract
We present a general theory for the full counting statistics of multiple Andreev reflections in incoherent superconducting-normal-superconducting contacts. The theory, based on a stochastic path integral approach, is applied to a superconductor-double-barrier system. It is found that all cumulants of the current show a pronounced subharmonic gap structure at voltages V=2Delta/en. For low voltages V<<Delta/e, the counting statistics results from diffusion of multiple charges in energy space, giving the pth cumulant Q(p) proportional, variantV(2-p), diverging for p> or =3. We show that this low-voltage result holds for a large class of incoherent superconducting-normal-superconducting contacts.
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Affiliation(s)
- S Pilgram
- Département de Physique Théorique, Universitè de Genéve, CH-1211, Genève 4, Switzerland
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Pala MG, Iannaccone G. Effect of dephasing on the current statistics of mesoscopic devices. PHYSICAL REVIEW LETTERS 2004; 93:256803. [PMID: 15697926 DOI: 10.1103/physrevlett.93.256803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2004] [Indexed: 05/24/2023]
Abstract
We investigate the effects of dephasing on the current statistics of mesoscopic conductors with a recently developed statistical model, focusing, in particular, on mesoscopic cavities and Aharonov-Bohm rings. For such devices, we analyze the influence of an arbitrary degree of decoherence on the cumulants of the current. We recover known results for the limiting cases of fully coherent and totally incoherent transport and are able to obtain detailed information on the intermediate regime of partial coherence for a varying number of open channels. We show that dephasing affects the average current, shot noise, and higher order cumulants in a quantitatively and qualitatively similar way, and that consequently shot noise or higher order cumulants of the current do not provide information on decoherence additional or complementary to what can be already obtained from the average current.
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Affiliation(s)
- Marco G Pala
- Dipartimento di Ingegneria dell'Informazione, Università degli Studi di Pisa, via Caruso, I-56122 Pisa, Italy
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Bodineau T, Derrida B. Current fluctuations in nonequilibrium diffusive systems: an additivity principle. PHYSICAL REVIEW LETTERS 2004; 92:180601. [PMID: 15169476 DOI: 10.1103/physrevlett.92.180601] [Citation(s) in RCA: 110] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2004] [Indexed: 05/24/2023]
Abstract
We formulate a simple additivity principle allowing one to calculate the whole distribution of current fluctuations through a large one dimensional system in contact with two reservoirs at unequal densities from the knowledge of its first two cumulants. This distribution (which in general is non-Gaussian) satisfies the Gallavotti-Cohen symmetry and generalizes the one predicted recently for the symmetric simple exclusion process. The additivity principle can be used to study more complex diffusive networks including loops.
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Affiliation(s)
- T Bodineau
- Laboratoire de Probabilités et Modèles Aléatoires, CNRS-UMR 7599, Universités Paris VI & VII, 4 place Jussieu, Case 188, F-75252 Paris Cedex 05, France.
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Distribution of transmitted charge through a double-barrier junction. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:8144-8149. [PMID: 9984495 DOI: 10.1103/physrevb.54.8144] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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