Related papers: Statistical Features of High-Dimensional Hamiltoni…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
In this thesis, we present a comprehensive study of chaos and thermalization of the one-dimensional Bose-Hubbard Model (BHM) within the classical field approximation. Two quantitative measures are compared: the ensemble-averaged Finite-time…
This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To…
Thermalization is the process through which a physical system evolves toward a state of thermal equilibrium. Determining whether or not a physical system will thermalize from an initial state has been a key question in condensed matter…
We study the dynamical and statistical behavior of the Hamiltonian Mean Field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is a simple toy model of $N$ fully-coupled rotators which…
The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical situations, relevant to condensed matter physics,…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
We examine the conjecture that entropy production in subsystems of a given system can be used as a dynamical criterion for quantum chaos in the latter. Numerical results are presented for finite dimensional spin systems as also for the…
Localization marks the breakdown of thermalization in subregions of quantum many-body systems in the presence of sufficiently large disorder. In this paper, we use numerical techniques to study thermalization and localization in a many-body…
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…
Several years after the pioneering work by Fermi Pasta and Ulam, fundamental questions about the link between dynamical and statistical properties remain still open in modern statistical mechanics. Particularly controversial is the role of…
By means of full exact diagonalization, we study level statistics and the structure of the eigenvectors of one-dimensional gapless bosonic and fermionic systems across the transition from integrability to quantum chaos. These systems are…
Recovering trajectories of quantum systems whose classical counterparts display chaotic behavior has been a subject that has received a lot of interest over the last decade. However, most of these studies have focused on driven and…
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger…
For nonautonomous Hamiltonian systems and their quantisations we discuss properties of the quantised systems, related to those of the corresponding classical systems, described by the KAM-related theories: the proper KAM, the averaging…
Quasi-integrable Hamiltonian systems are of great interest in many research fields of physics and mathematics. In these systems, the phase space has regular and chaotic trajectories. These trajectories depend in part on the magnitude of…
Decoherence in quantum systems which are classically chaotic is studied. It is well-known that a classically chaotic system when quantized loses many prominent chaotic traits. We show that interaction of the quantum system with an…
Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is,…
Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the…