Related papers: Chaos and Quantum Thermalization
The apparent randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations dynamically imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions…
Equilibrium properties of many-body systems with a large number of degrees of freedom are generally expected to be described by statistical mechanics. Such expectations are closely tied to the observation of thermalization, as manifested…
If a many-body quantum system approaches thermal equilibrium from a generic initial state, then the expectation value $\langle\psi(t)|A_i|\psi(t)\rangle$, where $|\psi(t)\rangle$ is the system's state vector and $A_i$ is an experimentally…
Berry conjecture is central to understanding quantum chaos in isolated systems and foundational for the eigenstate thermalization hypothesis. Here we establish an open-system analogy of the Berry conjecture, connecting quantum steady states…
We consider many-body quantum systems that exhibit quantum chaos, in the sense that the observables of interest act on energy eigenstates like banded random matrices. We study the time-dependent expectation values of these observables,…
Based on the view that thermal equilibrium should be characterized through macroscopic observations, we develop a general theory about typicality of thermal equilibrium and the approach to thermal equilibrium in macroscopic quantum systems.…
Time dynamics of isolated many-body quantum systems has long been an elusive subject. Very recently, however, meaningful experimental studies of the problem have finally become possible, stimulating theoretical interest as well. Progress in…
We study the problem of the approach to equilibrium in a macroscopic quantum system in an abstract setting. We prove that, for a typical choice of "nonequilibrium subspace", any initial state (from the energy shell) thermalizes, and in fact…
A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid…
We find non-monotonic equilibrium energy distributions, qualitatively different from the Fermi-Dirac and Bose-Einstein forms, in strongly-interacting many-body chaotic systems. The effect emerges in systems with finite energy spectra,…
The eigenstate thermalization hypothesis (ETH), which asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble, plays a pivotal role in understanding thermalization of isolated quantum…
An isolated quantum many-body system in an initial pure state will come to thermal equilibrium if it satisfies the eigenstate thermalization hypothesis (ETH). We consider alternatives to ETH that have been proposed. We first show that von…
We show that quantum chaotic many-body systems possess the thermodynamic arrow of time in the thermodynamic limit. Berry's conjecture in quantum chaotic systems and equivalence of ensembles imply the Kelvin statement of the second law of…
The fact that macroscopic systems approach thermal equilibrium may seem puzzling, for example, because it may seem to conflict with the time-reversibility of the microscopic dynamics. We here prove that in a macroscopic quantum system for a…
Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems. These are described by the two-body random ensemble, which is a paradigmatic…
The emergence of statistical mechanics for isolated classical systems comes about through chaotic dynamics and ergodicity. Here we review how similar questions can be answered in quantum systems. The crucial point is that individual energy…
Chaos and ergodicity are the cornerstones of statistical physics and thermodynamics. While classically even small systems like a particle in a two-dimensional cavity, can exhibit chaotic behavior and thereby relax to a microcanonical…
Understanding how macroscopic systems exhibit irreversible thermal behavior has been a long-standing challenge, first brought to prominence by Boltzmann. Recent advances have established rigorous conditions for isolated quantum systems to…
We consider an isolated, macroscopic quantum system. Let H be a micro-canonical "energy shell," i.e., a subspace of the system's Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + delta E. The…
It is shown that, by applying a principle of information theory, one obtains Berry's conjecture regarding the high-lying quantal energy eigenstates of classically chaotic systems.