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We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the…

The motion of charged particles in a crystal in the axial channeling regime can be both regular and chaotic. The chaos in quantum case manifests itself in the statistical properties of the energy levels set. These properties have been…

We consider a billiard model of a self-bound, interacting three-body system in two spatial dimensions. Numerical studies show that the classical dynamics is chaotic. The corresponding quantum system displays spectral fluctuations that…

Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…

We study the dynamical regimes demonstrated by a pair of identical 3-element ring oscillators (reduced version of synthetic 3-gene genetic Repressilator) coupled using the design of the "quorum sensing (QS)" process natural for…

We investigate a quantum algorithm which simulates efficiently the quantum kicked rotator model, a system which displays rich physical properties, and enables to study problems of quantum chaos, atomic physics and localization of electrons…

Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed…

Quantum dots pose a problem where one must confront three obstacles: randomness, interactions and finite size. Yet it is this confluence that allows one to make some theoretical advances by invoking three theoretical tools: Random Matrix…

The non-integrable Dicke model and its integrable approximation, the Tavis-Cummings (TC) model, are studied as functions of both the coupling constant and the excitation energy. The present contribution extends the analysis presented in the…

We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of the…

We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of "quantum chaotic dynamics". It is shown that under quite general conditions their roots…

A fundamental goal in the manipulation of quantum systems is the achievement of many coherent oscillations within the characteristic dephasing time T2*[1]. Most manipulations of electron spins in quantum dots have focused on the…

In this article, we study the classical chaotic scattering of a He atom off a harmonically vibrating Cu surface. The three degrees of freedom (3- dof) model is studied by first considering the non-vibrating 2-dof model for different values…

The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide…

Motivated by quantum gravity, semi-classical theory, and quantum theory on curved spacetimes, we study the system of an oscillator coupled to two spin-1/2 particles. This model provides a prototype for comparing three types of dynamics: the…

We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on…

We unveil chaotic behavior hidden in the energy spectrum of a Jahn-Teller ion vibrating in a cubic anharmonic potential as a typical model for rattling in cage-structure materials. When we evaluate the nearest-neighbor level-spacing…

In this paper, we study the dynamics of the interaction of a three-photon state and a quantum dot embedded in a semiconductor cavity. In the first place, we consider an ideal cavity in which the effects due to the environment are neglected.…

Decoherence in quantum systems which are classically chaotic is studied. The Arnold cat map and the quantum kicked rotor are chosen as examples of linear and nonlinear chaotic systems. The Feynman-Vernon influence functional formalism is…

Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the…