Related papers: Multiscale Structure of Eigenstate Thermalization
An isolated quantum system is said to thermalize if ${\rm Tr} (A \rho(t)) \to {\rm Tr} (A \rho_{\rm eq})$ for time $t \to \infty$. Here $\rho(t)$ is the time-dependent density matrix of the system, $\rho_{\rm eq}$ is the time-independent…
We study the emergence of statistical mechanics in isolated classical systems with local interactions and discrete phase spaces. We establish that thermalization in such systems does not require global ergodicity; instead, it arises from…
We show how the macroscopic state variables pressure, entropy and temperature of equilibrium thermodynamics can be consistently derived from the (quantum) chaotic spectral structure of one or two particles in two-dimensional domains. This…
We examine the majorization properties of general thermal-like mixed states depending on a set of parameters. Sufficient conditions which ensure the increase in mixedness, and hence of any associated entropic form, when these parameters are…
The eigenstate thermalization hypothesis (ETH) has been highly influential in explaining thermodynamic behavior of closed quantum systems. As of yet, it is unclear whether and how the ETH applies to non-Hermitian systems. Here, we introduce…
It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work,…
The Eigenstate-Thermalization-Hypothesis (ETH) has been established as the general framework to understand quantum statistical mechanics. Only recently has the attention been paid to so-called full ETH, which accounts for higher-order…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
This review is devoted to the problem of thermalization in a small isolated conglomerate of interacting constituents. A variety of physically important systems of intensive current interest belong to this category: complex atoms, molecules…
Under the Eigenstate Thermalization Hypothesis (ETH), quantum-quenched systems equilibrate towards canonical, thermal ensembles. While at first glance the ETH might seem a very strong hypothesis, we show that it is indeed not only…
It is believed that thermalization in closed systems of interacting particles can occur only when the eigenstates are fully delocalized and chaotic in the preferential (unperturbed) basis of the total Hamiltonian. Here we demonstrate that…
We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the eigenstates of the two-dimensional transverse field Ising model. By resolving all symmetries, we relate the onset of quantum chaos to the…
The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization.…
A class of autonomous quantum heat baths satisfying the eigenstate thermalization hypothesis (ETH) criteria is proposed. We show that such systems are expected to cause thermal relaxation of much smaller quantum systems coupled to one of…
The ETH ansatz for matrix elements of a given operator in the energy eigenstate basis results in a notion of thermalization for a chaotic system. In this context for a certain quantity - to be found for a given model - one may impose a…
We investigate dynamical equilibration of expectation values in closed quantum systems for realistic non-equilibrium initial states. Thereby we find that the corresponding long time expectation values depend on the initial expectation…
We consider the statistical properties of eigenstates of the time-evolution operator in chaotic many-body quantum systems. Our focus is on correlations between eigenstates that are specific to spatially extended systems and that…
Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual…
According to the eigenstate thermalization hypothesis (ETH), the eigenstate-to-eigenstate fluctuations of expectation values of local observables should decrease with increasing system size. In approaching the thermodynamic limit - the…
Many phases of matter, including superconductors, fractional quantum Hall fluids and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical…