Related papers: Thermalization in classical systems with discrete …
Thermalization of an isolated quantum system has been a nontrivial problem since the early days of quantum mechanics. In generic isolated quantum systems, nonequilibrium dynamics is expected to result in thermalization, indicating the…
Thermalization in closed quantum systems can be explained either by means of the eigenstate thermalization hypothesis or the concept of canonical typicality. Both concepts are based on quantum mechanical formalism such as spectral…
Using a Krylov-subspace time evolution algorithm, we simulate the real-time dynamics of translation invariant non-integrable finite spin rings to quite long times with high accuracy. We systematically study the finite-size deviation between…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
The dynamical evolution of neutrino flavor in supernovae can be modeled by an all-to-all spin Hamiltonian with random couplings. Simulating such two-local Hamiltonian dynamics remains a major challenge, as methods with controllable accuracy…
The eigenstate thermalization hypothesis provides to date the most successful description of thermalization in isolated quantum systems by conjecturing statistical properties of matrix elements of typical operators in the (quasi-)energy…
There is much interest in how quantum systems thermalize after a sudden change, because unitary evolution should preclude thermalization. The eigenstate thermalization hypothesis resolves this because all observables for quantum states in a…
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail)…
Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation. The equation significantly simplifies the complexities but describes essential information of…
The concept of entropy is fundamental to thermalization, yet appears at odds with basic principles in quantum mechanics. Statistical mechanics relies on the maximization of entropy for a system at thermal equilibrium. However, an isolated…
Under unitary time evolution, expectation values of physically reasonable observables often evolve towards the predictions of equilibrium statistical mechanics. The eigenstate thermalization hypothesis (ETH) states that this is also true…
This work studies the relationship between parametric amplification (or particle creation), adiabaticity and irreversibility in the non-quasi-static regime of a time-dependent quantum harmonic oscillator (TDHO) that evolves unitarily. We…
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…
The eigenstate thermalization hypothesis (ETH) provides a cornerstone for understanding thermalization in isolated quantum systems, linking quantum chaos with statistical mechanics. In this work, we extend the ETH framework to open quantum…
Proving thermalization from the unitary evolution of a closed quantum system is one of the oldest questions that is still nowadays only partially resolved. Several efforts have led to various formulations of what is called the eigenstate…
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…
We propose a generalization of the eigenstate thermalization hypothesis accounting for the emergence of symmetry-breaking phases. It consists of two conditions that any system with a degenerate spectrum must fulfill in order to thermalize.…
Recently, there have been significant new insights concerning conditions under which closed systems equilibrate locally. The question if subsystems thermalize---if the equilibrium state is independent of the initial state---is however much…
In an isolated quantum many-body system undergoing unitary evolution, we study the thermalization of a subsystem, treating the rest of the system as a bath. In this setting, the eigenstate thermalization hypothesis (ETH) was proposed to…
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…