Related papers: Quantum localization in rough billiards
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
The notion of a rough two-dimensional (convex) body is introduced, and to each rough body there is assigned a measure on $\TTT^3$ describing billiard scattering on the body. The main result is characterization of the set of measures…
For the representation of eigenstates on a Poincar\'e section at the boundary of a billiard different variants have been proposed. We compare these Poincar\'e Husimi functions, discuss their properties and based on this select one…
The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…
In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein-Gordon and Dirac equations in Rindler coordinates with…
The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions,…
The paper is devoted to the derivation of random unitary matrices whose spectral statistics is the same as statistics of quantum eigenvalues of certain deterministic two-dimensional barrier billiards. These random matrices are extracted…
We consider a strictly convex billiard table with $C^2$ boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection angle has a random perturbation. The perturbation…
We present experimental studies of the geometry-specific quantum scattering in microwave billiards of a given shape. We perform full quantum mechanical scattering calculations and find an excellent agreement with the experimental results.…
Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum…
The problem of the quantizations of the $L$-shaped billiards and the like ones, i.e. each angle of which is equal to $\pi/2$ or $3\pi/2$, is considered using as a tool the Fourier series expansion method. The respective wave functions and…
This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…
We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of super-diffusion, in the…
We work with the Friedrichs extension of a one dimensional Schrodinger whose potential has a certain type of regular singularity near one end point. We study the effect on the eigenvalues of shrinking the region slightly near the end point.…
We experimentally study a system of quantum kicked rotors - an ensemble of diatomic molecules exposed to a periodic sequence of ultrashort laser pulses. In the regime, where the underlying classical dynamics is chaotic, we investigate the…
A two-dimensional circular quantum billiard with unusual boundary conditions introduced by Berry and Dennis (\emph{J Phys A} {\bf 41} (2008) 135203) is considered in detail. It is demonstrated that most of its eigenfunctions are strongly…
We present numerical and experimental results for the development of islands of stability in atom-optics billiards with soft walls. As the walls are soften, stable regions appear near singular periodic trajectories in converging (focusing)…
The purpose of this article is to exploit the geometric structure of Quantum Mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that…
The zeroes of the Husimi function provide a minimal description of individual quantum eigenstates and their distribution is of considerable interest. We provide here a numerical study for pseudo- integrable billiards which suggests that the…
We examine the quantum mechanical eigensolutions of the two-dimensional infinite well or quantum billiard system consisting of a circular boundary with an infinite barrier or baffle along a radius. Because of the change in boundary…