Related papers: Quantum Mechanics of a Rotating Billiard
We study the motion of a charged quantum particle, constrained on the surface of a cylinder, in the presence of a radial magnetic field. When the spin of the particle is neglected, the system essentially reduces to an infinite family of…
We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular…
Quantum ergodicity of classically chaotic systems has been studied extensively both theoretically and experimentally, in mathematics, and in physics. Despite this long tradition we are able to present a new rigorous result using only…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
Triggered by a controversy surrounding a universal behaviour of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral…
The dynamics of three soft interacting particles on a ring is shown to correspond to the motion of one particle inside a soft triangular billiard. The dynamics inside the soft billiard depends only on the {\it masses ratio} between…
Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this…
In this paper we have tested several general numerical methods in solving the quantum billiards, such as the boundary integral method (BIM) and the plane wave decomposition method (PWDM). We performed extensive numerical investigations of…
We investigate the impact of internal spin on chaos in billiard systems. Extending the standard point-particle billiard by coupling translational and rotational degrees of freedom through a dimensionless spin parameter $\alpha = I/(mr^2)…
We perform numerical studies of the wave packet propagation through open quantum billiards whose classical counterparts exhibit regular and chaotic dynamics. We show that for t less or similar to tau (tau being the Heisenberg time), the…
We examine the quantum motion of two particles interacting through a contact force which are confined in a rectangular domain in two and three dimensions. When there is a difference in the mass scale of two particles, adiabatic separation…
This article reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor $T_{\alpha \beta}(x,y)$ for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the…
A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. Soft billiards are a generalization that includes a smooth boundary…
The coherent tunneling phenomenon is investigated in rectangular billiards divided into two domains by a classically unclimbable potential barrier. We show that by placing a pointlike scatterer inside the billiard, we can control the…
We construct an autonomous chaotic Hamiltonian ratchet as a channel billiard subdivided by equidistant walls attached perpendicularly to one side of the channel, leaving an opening on the opposite side. A static homogeneous magnetic field…
Dynamical properties of the elliptical stadium billiard, which is a generalization of the stadium billiard and a special case of the recently introduced mushroom billiards, are investigated analytically and numerically. In dependence on two…
In this article we study the dynamics of one-dimensional relativistic billiards containing particles with positive and negative energy. We study configurations with two identical positive masses and symmetric positions with two massless…
We assume that the level spectra of quantum systems in the initial phase of transition from integrability to chaos are approximated by superpositions of independent sequences. Each individual sequence is modeled by a random matrix ensemble.…
Recently, it has been demonstrated that asymptotic states of open quantum system can undergo qualitative changes resembling pitchfork, saddle-node, and period doubling classical bifurcations. Here, making use of the periodically modulated…
Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for…