Related papers: Statistical Features of High-Dimensional Hamiltoni…
We investigate chaotic behavior in a 2-D Hamiltonian system - oscillators with anharmonic coupling. We compare the classical system with quantum system. Via the quantum action, we construct Poincar\'e sections and compute Lyapunov exponents…
In quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Quite opposed, in classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between…
Von Neumann entropy production rates of the quantised kicked rotor interacting with an environment are calculated. A significant correspondence is found between the entropy contours of the classical and quantised systems. This is a…
We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian,…
A recent description of an exact map for the equilibrium structure and thermodynamics of a quantum system onto a corresponding classical system is summarized. Approximate implementations are constructed by pinning exact limits (ideal gas,…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…
Hypersensitivity to perturbation is a criterion for chaos based on the question of how much information about a perturbing environment is needed to keep the entropy of a Hamiltonian system from increasing. We demonstrate numerically that…
The emergence of statistical mechanics for isolated classical systems comes about through chaotic dynamics and ergodicity. Here we review how similar questions can be answered in quantum systems. The crucial point is that individual energy…
Generic signatures of quantum chaos found in realistic shell model calculations are compared with thermal statistical equilibrium. We show the similarity of the informational entropy of individual eigenfunctions in the mean field basis to…
The investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…
In a recent paper Roux [Phys. Rev. A 79, 021608(R) (2009), arXiv:0810.3720] argued that thermalization in a Bose-Hubbard system, after a quench, follows from the approximate Boltzmann distribution of the overlap between the initial state…
We study the threshold for chaos and its relation to thermalization in the 1D mean-field Bose-Hubbard model, which in particular describes atoms in optical lattices. We identify the threshold for chaos, which is finite in the thermodynamic…
The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of…
The dynamics of two-level systems in time-dependent backgrounds is under consideration. We present some new exact solutions in special backgrounds decaying in time. On the other hand, following ideas of Feynman, Vernon and Hellwarth, we…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble, whereas canonical ones fail in the most interesting, mostly inhomogeneous, situations like phase separations or away from the thermodynamic…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
We study the statistical and dynamical aspects of a translation-invariant Hamiltonian, without quench disorder, as an example of the manifestation of the phenomenon of many-body localization. This is characterized by the breakdown of…