Related papers: Towards local equilibration in closed interacting …
For a quantum system to be captured by a stationary statistical ensemble, as is common in thermodynamics and statistical mechanics, it is necessary that it reaches some apparently stationary state in the first place. In this book chapter,…
Isolated many-body quantum systems quenched far from equilibrium can eventually equilibrate, but it is not yet clear how long they take to do so. To answer this question, we use exact numerical methods and analyze the entire evolution, from…
We show that the physical mechanism for the equilibration of closed quantum systems is dephasing, and identify the energy scales that determine the equilibration timescale of a given observable. For realistic physical systems (e.g those…
We consider isolated many-body quantum systems which do not thermalize, i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A…
We address the problem of understanding from first principles the conditions under which a quantum system equilibrates rapidly with respect to a concrete observable. On the one hand previously known general upper bounds on the time scales…
It has recently been shown that small quantum subsystems generically equilibrate, in the sense that they spend most of the time close to a fixed equilibrium state. This relies on just two assumptions: that the state is spread over many…
One of the outstanding problems in non-equilibrium physics is to precisely understand when and how physically relevant observables in many-body systems equilibrate under unitary time evolution. General equilibration results show that…
An analytical prediction is established of how an isolated many-body quantum system relaxes towards its thermal long-time limit under the action of a time-independent perturbation, but still remaining sufficiently close to a reference case…
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…
We investigate the equilibration of an isolated macroscopic quantum system in the sense that deviations from a steady state become unmeasurably small for the overwhelming majority of times within any sufficiently large time interval. The…
We investigate the equilibration and thermalization properties of quantum systems interacting with a finite dimensional environment. By exploiting the concept of time averaged states, we introduce a completely positive map which allows to…
In quantum statistical mechanics, closed many-body systems that do not exhibit thermalization after an arbitrarily long time in spite of the presence of interactions are called as many-body localized systems, and recently have been…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on…
Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…
We characterize the conditions under which a multi-time quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a…
Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions…
The self-averaging behavior of interacting many-body quantum systems has been mostly studied at equilibrium. The present work addresses what happens out of equilibrium, as the increase of the strength of onsite disorder takes the system to…
The local equilibration time of quantum many-body systems has been conjectured to satisfy a `Planckian bound', $\tau_{\rm eq}\gtrsim \frac{\hbar}{T}$. We provide a sharp and universal definition of this time scale, and show that it is…
This chapter discusses the conditions and timescales under which isolated many-body quantum systems, initially far from equilibrium, ultimately reach thermal equilibrium. We also examine quantities that, during the relaxation process,…
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state…