Relaxation and Thermalization of Isolated Many-Body Quantum Systems

Abstract

We provide an overview of our numerical and analytical studies of isolated interacting quantum systems that are quenched out of equilibrium instantaneously. We describe the relaxation process to a new equilibrium and obtain lower bounds for the relaxation time of full random matrices and realistic systems with two-body interactions. We show that the size of the time fluctuations after relaxation decays exponentially with system size for systems without too many degeneracies. We also discuss the conditions for thermalization and demonstrate that it can happen after local and global quenches in space. The analyses are developed for systems, initial states, and few-body observables accessible to experiments with optical lattices.

11 pages, 6 figures. This is an overview of our previous works submitted to the FQMT13 special volume of the Physica Scripta

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Cited by in corpus (35)

• Quantum many-body systems out of equilibrium
• Thouless and relaxation time scales in many-body quantum systems
• Eigenstate Thermalization in a Locally Perturbed Integrable System
• Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance and out-of-time-ordered correlator
• Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• Dynamical Manifestations of Quantum Chaos: Correlation Hole and Bulge
• Thermalization of dilute impurities in one dimensional spin chains
• Inevitable Power-law Behavior of Isolated Many-Body Quantum Systems and How It Anticipates Thermalization
• Speck of Chaos
• Power-law decay exponents: a dynamical criterion for predicting thermalization
• Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
• Realistic many-body quantum systems vs full random matrices: static and dynamical properties
• Quantum coherence as a signature of chaos
• Equilibration towards generalized Gibbs ensembles in non-interacting theories
• Many-Body Dephasing in a Trapped-Ion Quantum Simulator
• Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems
• Degenerate observables and the many Eigenstate Thermalization Hypotheses
• Many-particle dephasing after a quench
• Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase
• Level Repulsion and Dynamics in the Finite One-Dimensional Anderson Model
• Decay of a Thermofield-Double State in Chaotic Quantum Systems
• Transport through interacting defects and lack of thermalisation
• Signatures of chaos and thermalization in the dynamics of many-body quantum systems
• Self-averaging in many-body quantum systems out of equilibrium: Time dependence of distributions
• How many particles make up a chaotic many-body quantum system?
• Taking snapshots of a quantum thermalization process: emergent classicality in quantum jump trajectories
• Survival Probability of the Néel State in Clean and Disordered Systems: an Overview
• Weak ergodicity breaking in Josephson-junction arrays
• Canonical density matrices from eigenstates of mixed systems
• Nonequilibrium many-body quantum dynamics: from full random matrices to real systems
• New equilibrium ensembles for isolated quantum systems
• Dynamics of Coherent States in Regular and Chaotic Regimes of the Non-integrable Dicke Model
• Hierarchy of timescales in a disordered spin-$1/2$ XX ladder
• Ballistic propagation of a local impact in the one-dimensional $XY$ model
• Boundary Chaos: Spectral Form Factor