Related papers: Quantum ergodicity in mixed and KAM Hamiltonian sy…
Quantum chaos is a quantum many-body phenomenon that is associated with a number of intricate properties, such as level repulsion in energy spectra or distinct scalings of out-of-time ordered correlation functions. In this work, we…
In these lecture notes we review some recent attempts at searching for non-Fermi liquids and novel quantum phase transitions in holographic systems using gauge/gravity duality. We do this by studying the simplest finite density system…
We show that some $C^*$--dynamical systems obtained by "quantizing" classical ones on the free Fock space, enjoy very strong ergodic properties. Namely, if the classical dynamical system $(X, T, \m)$ is ergodic but not weakly mixing, then…
In this paper we investigate a class of natural Hamiltonian systems with two degrees of freedom. The kinetic energy depends on coordinates but the system is homogeneous. Thanks to this property it admits, in a general case, a particular…
Two-dimensional decaying turbulent flow is known to approach apparently stable states after a long time evolution. A few theories and models have been so far proposed to account for this relaxation. In this paper, we compare results of…
The {\it curvature} and the {\it reduced curvature} are basic differential invariants of the pair: (Hamiltonian system, Lagrange distribution) on the symplectic manifold. We show that negativity of the curvature implies that any bounded…
Billiards are flat cavities where a particle is free to move between elastic collisions with the boundary. In chaos theory these systems are simple prototypes, their conservative dynamics of a billiard may vary from regular to chaotic,…
It has been recently argued that near-integrable nonautonomous one-degree-of-freedom Hamiltonian systems are constrained by KAM theory even when the time-dependent (nonintegrable) part of the Hamiltonian is given in the form of a…
We consider the quantization of the midi-superspace associated with a class of spacetimes with toroidal isometries, but without the compact spatial hypersurfaces of the well-known Gowdy models. By a symmetry reduction, the phase space for…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
We investigate the thermodynamic behavior of open quantum systems through the Hamiltonian of Mean Force, focusing on two models: a two-qubit system interacting with a thermal bath and a Jaynes-Cummings Model without the rotating wave…
We study thermalization in many-body quantum systems locally coupled to an external bath. It is shown that quantum chaotic systems do thermalize, that is, they exhibit relaxation to an invariant ergodic state which, in the bulk, is well…
A family of classical integrable systems defined on a deformation of the two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed through Hamiltonians defined on the non-standard quantum deformation of a sl(2) Poisson…
In this paper we show that the quantum theory of chaos, based on the statistical theory of energy spectra, presents inconsistencies difficult to overcome. In classical mechanics a system described by an hamiltonian $H = H_1 + H_2$…
We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum…
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…
In this work we report on a loss of ergodicity in a simple hopping model, motivated by the Hubbard Hamiltonian, of a many body quantum system at zero temperature, quantized in Euclidean time. We show that this quantum system may lose…
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…
We study the aspects of quantum chaos in mushroom billiards introduced by Bunimovich. This family of billiards classically has the property of mixed phase space with precisely one entirely regular and one fully chaotic (ergodic) component,…
Recent works have established universal entanglement properties and demonstrated validity of single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians. However, a common property of all quantum-chaotic quadratic…