4.8 Article

Bogoliubov-Born-Green-Kirkwood-Yvon Hierarchy and Generalized Hydrodynamics

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Editorial Material Mechanics

Introduction to the Special Issue on Emergent Hydrodynamics in Integrable Many-Body Systems

Alvise Bastianello et al.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2022)

Article Mechanics

Correlation functions and transport coefficients in generalised hydrodynamics

Jacopo De Nardis et al.

Summary: This article reviews recent advances in exact results for dynamical correlation functions and related transport coefficients in interacting integrable models at large scales. The discussion includes topics such as Drude weights, conductivity and diffusion constants, as well as linear and nonlinear response in equilibrium and non-equilibrium states. The authors consider the problems from the perspectives of the general hydrodynamic theory of many-body systems and form-factor expansions in integrable models, showing how they provide a comprehensive and consistent set of exact methods for extracting large scale behaviors. Various applications in integrable spin chains and field theories are also discussed.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2022)

Article Mechanics

Generalized hydrodynamics in the one-dimensional Bose gas: theory and experiments

Isabelle Bouchoule et al.

Summary: This article reviews the recent progress in the generalized hydrodynamics (GHD) behavior of the one-dimensional Bose gas with contact repulsive interactions, known as the Lieb-Liniger gas. The theory and key concepts of the Lieb-Liniger gas, including rapidities and rapidity distribution, are introduced. The asymptotic regimes and approximate descriptions of the Lieb-Liniger gas are presented. Experimental results in cold atom experiments, including the realization of the Lieb-Liniger model and tests of the GHD theory, are discussed. The effects of atom losses and some open questions are also reviewed.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2022)

Article Physics, Multidisciplinary

Duality between Weak and Strong Interactions in Quantum Gases

Etienne Granet et al.

Summary: In one-dimensional quantum gases, there is a duality between hard core bosons and noninteracting fermions. However, the exact duality connecting strongly interacting bosons to weakly interacting fermions is still unknown at the field theory level. This study proposes a solution to this problem by regularizing the pointlike interaction between fermions in one dimension, which induces a discontinuity in the wave function proportional to its derivative. By introducing a weak potential for small interaction strengths, standard methods of diagrammatic perturbation theory can be applied to strongly interacting bosons.

PHYSICAL REVIEW LETTERS (2022)

Article Physics, Multidisciplinary

Out-of-equilibrium dynamics of the XY spin chain from form factor expansion

Etienne Granet et al.

Summary: We study the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. By considering a particular subset of Gaussian states called Coherent Ensemble (CE), we propose a natural and unified framework for describing out-of-equilibrium physics in this model. We establish that all correlation functions in the CE can be computed using form factor expansion and are expressible in terms of Fredholm determinants. Specifically, we derive exact out-of-equilibrium expressions in the thermodynamic limit for the previously unknown order parameter 1-point function, dynamical 2-point function, and equal-time 3-point function.

SCIPOST PHYSICS (2022)

Article Physics, Multidisciplinary

Quasiparticle kinetic theory for Calogero models

Vir B. Bulchandani et al.

Summary: In both quantum and classical Calogero models, the quasiparticle kinetic theory reduces to the free-streaming Boltzmann equation. A Bethe-Lax correspondence is developed in the classical case to reconcile the simple emergent behavior with the strongly interacting character of the model. This framework provides a simple description of multi-soliton solutions in a harmonic trap, showing excellent agreement with numerical simulations for both integrable and non-integrable cases.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2021)

Article Mechanics

Form factors and generalized hydrodynamics for integrable systems

Axel Cortes Cubero et al.

Summary: Our review covers the microscopic foundations of Generalized Hydrodynamics (GHD) through form factor expansions and the availability of a self-conserved current as two orthogonal approaches.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2021)

Article Mechanics

Hydrodynamics of weak integrability breaking

Alvise Bastianello et al.

Summary: The article reviews recent progress in understanding nearly integrable models within the framework of generalized hydrodynamics (GHD). It discusses the thermalization process after integrability is broken and the transition from GHD to standard hydrodynamics.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2021)

Article Mechanics

Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects

Vincenzo Alba et al.

Summary: This paper provides a pedagogical introduction to the generalized hydrodynamic approach in inhomogeneous quenches in integrable many-body quantum systems, focusing on applications to bipartitioning protocols and trap quenches. Exact results for time-dependent correlation functions and entanglement evolution are discussed, as well as the theory's range of applicability, open questions, and future directions.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2021)

Article Physics, Multidisciplinary

Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54

Katja Klobas et al.

Summary: The study investigates the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 using a time-channel approach, demonstrating a family of non-equilibrium product states and proving that finite subsystems relax to a one-parameter family of Gibbs states. In addition, inhomogeneous quenches are considered, showing that finite subsystems eventually relax to the non-equilibrium steady state predicted by generalised hydrodynamics when prepared in two different solvable states. This is the first exact description of relaxation to a NESS in an interacting system, providing independent confirmation of generalised hydrodynamics for an inhomogeneous quench.

SCIPOST PHYSICS (2021)

Article Physics, Multidisciplinary

Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model

Etienne Granet et al.

Summary: In this study, we investigated the time evolution of local observables in the repulsive Lieb-Liniger model after an interaction quench using the Quench Action approach. By deriving a 1/c expansion for various one and two-point functions, we confirmed the typicality assumptions underlying the Quench Action approach. Our results provide a non-trivial confirmation of the typicality assumptions and contribute to our understanding of quantum systems.

SCIPOST PHYSICS (2021)

Article Physics, Multidisciplinary

Exact Thermalization Dynamics in the Rule 54 Quantum Cellular Automaton

Katja Klobas et al.

Summary: In this study, the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 was examined, revealing the full thermalization dynamics at a microscopic level using simple quantum channels for low-entangled initial states. Analytic formulas for the evolution of local observables and Renyi entropies were provided, showing that Rule 54 does not behave as a simple Markovian bath and exhibits nonequilibrium features of interacting integrable many-body quantum systems. This study offers a rare example where the entire thermalization dynamics can be exactly solved at the microscopic level.

PHYSICAL REVIEW LETTERS (2021)

Review Physics, Multidisciplinary

Finite-temperature transport in one-dimensional quantum lattice models

B. Bertini et al.

Summary: Significant progress has been made in the theoretical understanding of transport properties in one-dimensional quantum lattice systems in the past decade, with Bethe-ansatz integrable models and novel simulation methods playing important roles. The discovery of quasilocal conserved quantities provides insight into the origins of finite-temperature transport behavior, while state-of-the-art theoretical methods, including matrix-product-state-based simulation and generalized hydrodynamics, are discussed. The close connection between theoretical models and recent experiments, particularly in the context of quantum magnets and ultracold quantum gases in optical lattices, is also highlighted.

REVIEWS OF MODERN PHYSICS (2021)

Review Mechanics

Current operators in integrable models: a review

Marton Borsi et al.

Summary: This article primarily discusses the current operators of one-dimensional integrable models and their crucial role in generalized hydrodynamics, including mean currents in finite volume and in the thermodynamic limit. The review also presents some new research findings, such as computing the currents of the Heisenberg spin chains using the string hypothesis.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2021)

Review Physics, Multidisciplinary

Quantum many-body scars and weak breaking of ergodicity

Maksym Serbyn et al.

Summary: Thermalization is the inevitable fate of many complex quantum systems, but recent discoveries have shown the existence of a new type of behavior called quantum many-body scarring, where the system rapidly relaxes for most initial conditions, yet certain initial states display non-ergodic dynamics. This phenomenon, similar to scars observed in single-particles in specific potentials, has potential applications in quantum technology.

NATURE PHYSICS (2021)

Article Physics, Multidisciplinary

Nonequilibrium Dynamics and Weakly Broken Integrability

Joseph Durnin et al.

Summary: Motivated by experiments on cold atomic gases, a quantum kinetic approach to weakly perturbed integrable models out of equilibrium is developed. Using exact matrix elements, an analytical approach to real-time dynamics is established, providing predictions for physical quantities' time evolution and conceptual links between quantum many-body dynamics and classical theory. Specific perturbations that do not cause thermalization in the weakly perturbed regime are identified.

PHYSICAL REVIEW LETTERS (2021)

Article Multidisciplinary Sciences

Generalized hydrodynamics in strongly interacting 1D Bose gases

Neel Malvania et al.

Summary: The theory of generalized hydrodynamics (GHD) shows promise in efficiently simulating nearly integrable systems, as demonstrated in experiments with ultracold 1D Bose gases. The results indicate that GHD can accurately describe the quantum dynamics of such systems, even with low particle numbers and rapid density changes.

SCIENCE (2021)

Article Materials Science, Multidisciplinary

Hydrodynamics of nonintegrable systems from a relaxation-time approximation

Javier Lopez-Piqueres et al.

Summary: The study developed a general kinetic theory framework to describe the hydrodynamics of strongly interacting, nonequilibrium quantum systems, employing a generalized relaxation-time approximation for computing nonequilibrium transport with surprisingly accurate results. Despite its simplicity, the framework was able to capture phenomena unique to strongly interacting systems, such as distinct charge and energy diffusion constants.

PHYSICAL REVIEW B (2021)

Article Physics, Multidisciplinary

Quantum Generalized Hydrodynamics

Paola Ruggiero et al.

PHYSICAL REVIEW LETTERS (2020)

Article Physics, Multidisciplinary

A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model

Etienne Granet et al.

SCIPOST PHYSICS (2020)

Article Materials Science, Multidisciplinary

Diffusive hydrodynamics from integrability breaking

Aaron J. Friedman et al.

PHYSICAL REVIEW B (2020)

Article Physics, Multidisciplinary

Locally quasi-stationary states in noninteracting spin chains

Maurizio Fagotti

SCIPOST PHYSICS (2020)

Article Materials Science, Multidisciplinary

Exact dynamics in dual-unitary quantum circuits

Lorenzo Piroli et al.

PHYSICAL REVIEW B (2020)

Article Physics, Multidisciplinary

Generalized Hydrodynamics on an Atom Chip

M. Schemmer et al.

PHYSICAL REVIEW LETTERS (2019)

Article Physics, Multidisciplinary

Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos

Bruno Bertini et al.

PHYSICAL REVIEW X (2019)

Article Physics, Multidisciplinary

Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions

Alvise Bastianello et al.

PHYSICAL REVIEW LETTERS (2019)

Article Multidisciplinary Sciences

Quantum supremacy using a programmable superconducting processor

Frank Arute et al.

NATURE (2019)

Article Physics, Multidisciplinary

Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit

Krishnanand Mallayya et al.

PHYSICAL REVIEW LETTERS (2018)

Article Materials Science, Multidisciplinary

Higher-order generalized hydrodynamics in one dimension: The noninteracting test

Maurizio Fagotti

PHYSICAL REVIEW B (2017)

Article Physics, Multidisciplinary

A note on generalized hydrodynamics: inhomogeneous fields and other concepts

Benjamin Doyon et al.

SCIPOST PHYSICS (2017)

Article Mechanics

Quench dynamics and relaxation in isolated integrable quantum spin chains

Fabian H. L. Essler et al.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2016)

Editorial Material Mechanics

Introduction to 'Quantum Integrability in Out of Equilibrium Systems'

Pasquale Calabrese et al.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2016)

Article Mechanics

Generalized Gibbs ensemble in integrable lattice models

Lev Vidmar et al.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2016)

Article Physics, Multidisciplinary

Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents

Bruno Bertini et al.

PHYSICAL REVIEW LETTERS (2016)

Review Physics, Multidisciplinary

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems

Christian Gogolin et al.

REPORTS ON PROGRESS IN PHYSICS (2016)

Article Physics, Multidisciplinary

Emergent Hydrodynamics in Integrable Quantum Systems Out of Equilibrium

Olalla A. Castro-Alvaredo et al.

PHYSICAL REVIEW X (2016)

Article Physics, Multidisciplinary

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases

G. P. Brandino et al.

PHYSICAL REVIEW X (2015)

Article Mathematics, Applied

From Boltzmann's Equation to the Incompressible Navier-Stokes-Fourier System with Long-Range Interactions

Diogo Arsenio

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2012)

Article Multidisciplinary Sciences

Localization and Glassy Dynamics Of Many-Body Quantum Systems

Giuseppe Carleo et al.

SCIENTIFIC REPORTS (2012)

Article Physics, Multidisciplinary

The density-matrix renormalization group in the age of matrix product states

Ulrich Schollwoeck

ANNALS OF PHYSICS (2011)

Article Physics, Multidisciplinary

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

Anatoli Polkovnikov et al.

REVIEWS OF MODERN PHYSICS (2011)

Article History & Philosophy Of Science

Proof of the ergodic theorem and the H-theorem in quantum mechanics

J. von Neumann

EUROPEAN PHYSICAL JOURNAL H (2010)

Article Multidisciplinary Sciences

Thermalization and its mechanism for generic isolated quantum systems

Marcos Rigol et al.

NATURE (2008)

Review Physics, Multidisciplinary

Many-body physics with ultracold gases

Immanuel Bloch et al.

REVIEWS OF MODERN PHYSICS (2008)

Article Mechanics

Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces -: art. no. P04005

AJ Daley et al.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2004)

Article Physics, Multidisciplinary

Real-time evolution using the density matrix renormalization group

SR White et al.

PHYSICAL REVIEW LETTERS (2004)

Article Physics, Mathematical

On the quantum Boltzmann equation

L Erdös et al.

JOURNAL OF STATISTICAL PHYSICS (2004)