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Starting from a microscopic description of weak system-bath interactions, we derive from first principles a quantum master equation that does not rely on the well-known rotating wave approximation. This includes generic many-body systems,…
An exact stochastic model for the thermalisation of quantum states is proposed. The model has various physically appealing properties. The dynamics are characterised by an underlying Schrodinger evolution, together with a nonlinear term…
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…
Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, resolving the apparent incongruity between the reversibility of Schr\"odinger's equation and the second law of thermodynamics. Despite…
The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has…
We present quantitative predictions for quantum simulator experiments on Ising models from trapped ions to Rydberg chains and show how the thermalization, and thus decoherence times, can be controlled by considering common, independent, and…
Open quantum systems that comply with the master equation and detailed balance decay in a non-oscillatory manner to thermal equilibrium. Beyond the weak coupling limit, systems that break microreversibility (e.g., in the presence of…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge in studying such non-equilibrium dynamics is the scarcity of experimental tools for characterizing their complex transient states.…
We study the emergence over time of a universal, uniform distribution of quantum states supported on a finite subsystem, induced by projectively measuring the rest of the system. Dubbed deep thermalization, this phenomenon represents a form…
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…
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…
Quantum detailed balance conditions and quantum fluctuation relations are two important concepts in the dynamics of open quantum systems: both concern how such systems behave when they thermalize because of interaction with an environment.…
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…
The last decade has witnessed the remarkable progress in our understanding of thermalization in isolated quantum systems. Combining the eigenstate thermalization hypothesis with quantum measurement theory, we extend the framework of quantum…
State-of-the-art quantum simulators permit local temporal control of interactions and midcircuit readout. These capabilities open the way towards the exploration of intriguing nonequilibrium phenomena. We illustrate this with a kinetically…
We discuss how the thermalization of an elementary quantum system is modified when the system is placed in an environment out of thermal equilibrium. To this aim we provide a detailed investigation of the dynamics of an atomic system placed…
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…
One explanation of the thermalization of an isolated quantum system is the eigenstate thermalization hypothesis, which posits that all energy eigenstates are thermal. Based on this idea, we use dynamical typicality to predict the thermal…
Understanding how closed quantum systems dynamically approach thermal equilibrium presents a major unresolved problem in statistical physics. Generically, non-integrable quantum systems are expected to thermalize as they comply with the…