We consider the question of thermalization for isolated quantum systems after a sudden parameter change, a so-called quantum quench. In part icular we investigate the pre-requisites for thermalization focusing on the statistical properties of the time-averaged density matrix and o f the expectation values of observables in the final eigenstates. We find that eigenstates, which are rare compared to the typical ones sampled by the micro-canonical distribution, are responsible for the absence of thermalization of some infinite integrable models and play an important role for some non-integrable systems of finite size, such as the Bose-Hubbard model. We stress the importance of finite size effects for the thermalization of isolated quantum systems and discuss two alternative scenarios for thermalization, as well as ways to prune down the correct one.
Thermalization in an isolated oscillating Bose-Einstein condensate in a disordered trap is investigated. We show Shannon entropy in $x$ or $p$ representation is the eligible one to describe the thermalization. Besides, we show that multiple scattering with the disorder generates more and more incoherent thermal particles and condensed and thermal particles act as mutual heat bath that results in the thermalization of the whole system. We also demonstrate that Loschmidt's paradox can be resolved in the present system.
The dynamics of a many-body system can take many forms, from a purely reversible evolution to fast thermalization. Here we show experimentally and numerically that an assembly of spin 1 atoms all in the same spatial mode allows one to explore this wide variety of behaviors. When the system can be described by a Bogoliubov analysis, the relevant energy spectrum is linear and leads to undamped oscillations of many-body observables. Outside this regime, the non-linearity of the spectrum leads to irreversibity, characterized by a universal behavior. When the integrability of the Hamiltonian is bro…
We study dynamics of entanglement in the thermalization process of an isolated quantum many-body system. We propose a simple setup for measuring the propagation speed of entanglement entropy (EE) in numerical simulations and apply it to the integrable/non-integrable spin models in 1D - the transverse Ising (TI) model, the chaotic Ising (CI) model, and the extended chaotic Ising (ECI) model. We find that two distinct time-scales $t^\ast$ and $t_{\rm {diff}}$ arise in the dynamics of EE in the thermalization process: the former represents the time-scale for the saturation of EE and the latter ch…
The postulates of the eigenstate thermalization hypothesis (ETH) express that thermalization occurs due to the individual eigenstate of the system's Hamiltonian. But the ETH put no light on the dynamics that lead toward thermalization. In this paper, we observe the thermalization of a Bose-Einstein Condensate (BEC) confined in an optical lattice potential that is embedded in the harmonic trap. Such optical lattice potential offers local friction to the oscillating BEC. The spread in the temporal density plot of BEC shows the thermalization of the BEC. Moreover, we observe that the presence of …
Prethermalization has been extensively studied in systems close to integrability. We propose a more general, yet conceptually simpler, setup for this phenomenon. We consider a---possibly nonintegrable---reference dynamics, weakly perturbed so that the perturbation breaks at least one conservation law of the reference dynamics. We argue then that the evolution of the system proceeds via intermediate (generalized) equilibrium states of the reference dynamics. The motion on the manifold of equilibrium states is governed by an autonomous equation, flowing towards global equilibrium in a time of or…
Integrable systems do not obey the strong eigenstate thermalization hypothesis (ETH), which has been proposed as a mechanism of thermalization in isolated quantum systems. It has been suggested that an integrable system reaches a steady state described by a generalized Gibbs ensemble (GGE) instead of thermal equilibrium. We prove that a generalized version of the strong ETH holds for noninteracting integrable systems with translation invariance. Our generalized ETH states that any pair of energy eigenstates with similar values of local conserved quantities looks similar with respect to local o…
Understanding quantum thermalization through entanglement build-up in isolated quantum systems addresses fundamental questions on how unitary dynamics connects to statistical physics. Here, we study the spin dynamics and approach towards local thermal equilibrium of a macroscopic ensemble of S = 3 spins prepared in a pure coherent spin state, tilted compared to the magnetic field, under the effect of magnetic dipole-dipole interactions. The experiment uses a unit filled array of 104 chromium atoms in a three dimensional optical lattice, realizing the spin-3 XXZ Heisenberg model. The buildup of…
We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai-oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that for a many-body system of cold atoms the interactions, with a strength above a certain quantum chaos border given by the Aberg criterion, lead to the Fermi-Dirac distribution and relaxation of many-body initial states to the thermalized state in absence of any contact with a thermostate. We discuss the properties of this dynamical thermalization and its links w…
We investigate the detailed properties of Observational entropy, introduced by Šafránek et al. [Phys. Rev. A 99, 010101 (2019)] as a generalization of Boltzmann entropy to quantum mechanics. This quantity can involve multiple coarse-grainings, even those that do not commute with each other, without losing any of its properties. It is well-defined out of equilibrium, and for some coarse-grainings it generically rises to the correct thermodynamic value even in a genuinely isolated quantum system. The quantity contains several other entropy definitions as special cases, it has interesting informa…
Quantum many-body scar (QMBS) and quantum integrability(QI) have been recognized as two distinct mechanisms for the breakdown of eigenstate thermalization hypothesis(ETH) in an isolated system. In this work, we reveal a smooth route to connect these two ETH-breaking mechanisms in the Ising chain with transverse and longitudinal fields. Specifically, starting from an initial Ising anti-ferromagnetic state, we find that the dynamical system undergoes a smooth non-thermal crossover from QMBS to QI by changing the Ising coupling($J$) and longitudinal field($h$) simultaneously while keeping their r…
Thermalizing quantum systems are conventionally described by statistical mechanics at equilibrium. However, not all systems fall into this category, with many body localization providing a generic mechanism for thermalization to fail in strongly disordered systems. Many-body localized (MBL) systems remain perfect insulators at non-zero temperature, which do not thermalize and therefore cannot be described using statistical mechanics. In this Colloquium we review recent theoretical and experimental advances in studies of MBL systems, focusing on the new perspective provided by entanglement and …
Thermalization is a ubiquitous process of statistical physics, in which details of few-body observables are washed out in favor of a featureless steady state. Even in isolated quantum many-body systems, limited to reversible dynamics, thermalization typically prevails. However, in these systems, there is another possibility: many-body localization (MBL) can result in preservation of a non-thermal state. While disorder has long been considered an essential ingredient for this phenomenon, recent theoretical work has suggested that a quantum many-body system with a uniformly increasing field -- b…
