Related papers: Statistical Features of High-Dimensional Hamiltoni…
Recent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-point functions, at least for maximally chaotic…
Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems, made up of microscopic particles, in terms of a small number of macroscopic quantities, such as…
In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now named by the more fashionable term of deterministic…
Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
We study the effects of dissipation and decoherence induced on a harmonic oscillator by the coupling to a chaotic system with two degrees of freedom. Using the Feynman-Vernon approach and treating the chaotic system semiclassically we show…
Linking thermodynamic variables like temperature $T$ and the measure of chaos, the Lyapunov exponents $\lambda$, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions,…
We formulate a canonical quantization of Equilibrium Thermodynamics by applying Dirac's theory of constrained systems. Thermodynamic variables are treated as conjugate pairs of coordinates and momenta, allowing extensive and intensive…
The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic non-integrable ones. While diagonal matrix elements for…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
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…
The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the…
It is argued that the two problems of choosing characterizations and models of complex systems should not be considered independently. A particular criterion for these choices, oriented on the potential usefulness of the results, is…
Eigenstate thermalization hypothesis is a detailed statement of the matrix elements of few-body operators in energy eigenbasis of a chaotic Hamiltonian. Part of the statement is that the off-diagonal elements fall exponential for large…
We analyze a new class of time-periodic nonreciprocal dynamics in interacting chaotic classical spin systems, whose equations of motion are conservative (phase-space-volume-preserving) yet possess no symplectic structure. As a result, the…
Thermal equilibrium states of many-body Hamiltonians are essential for probing quantum chaos, finite-temperature phases of matter, and training quantum machine learning models, yet generating large collections of such states across…