Related papers: Evolving momentum-projected densities in billiards…

We examine high energy eigenfunctions for the Dirichlet Laplacian on domains where the billiard flow exhibits mixed dynamical behavior. (More generally, we consider semiclassical Schrodinger operators with mixed assumptions on the…

We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three…

Rational polygonal billiards are one of the key models among the larger class of pseudo-integrable billiards. Their billiard flow may be lifted to the geodesic flow on a translation surface. Whereas such classical billiards have been much…

The evolution of the phase space density of particle beams in external fields is found proceeding from the continuity equation in the six-dimensional (6D) phase space (mu-space). The Robinson theorem, which includes the Liouville theorem as…

By analytical mapping of the eigenvalue problem in rough billiards on to a band random matrix model a new regime of Wigner ergodicity is found. There the eigenstates are extended over the whole energy surface but have a strongly peaked…

We study the convergence towards the equilibrium for a dissipative and stochastic time-dependent oval billiard. The dynamics of the system is described by using a generic four dimensional nonlinear map for the variables: the angular…

We introduce a new method for estimating the growth of various quantities arising in dynamical systems. We apply our method to polygonal billiards on surfaces of constant curvature. For instance, we obtain power bounds of degree two plus…

Numerical experiments of the statistical evolution of an ensemble of non-interacting particles in a time-dependent billiard with inelastic collisions, reveals the existence of three statistical regimes for the evolution of the speeds…

This paper is concerned with the study of one-body dissipation effects in idealized models resembling a nucleus. In particular, we study the quantum mechanics of a free particle that collides elastically with the slowly moving walls of a…

We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…

This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new…

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…

In this paper we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a 2-dimensional conservative and reversible dynamical system, defined by a Twist diffeomorphism,…

This paper presents a novel formalism for the out of equilibrium dynamics of the density matrix, capable of describing highly entangled many-body interactions. The evolution of quantum states is evaluated via eigenvalue dynamics of a…

We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes…

We calculate the density P(\tau) of the eigenvalues of the Wigner-Smith time delay matrix for two-dimensional rectangular and circular billiards with one opening. For long times, the density of these so-called "proper delay times" decays…

We investigate a circular cavity billiard within which a pair of identical hard disks of smaller but finite size is confined. Each disk shows a free motion except when bouncing elastically with its partner and with the boundary wall.…

The problem of two interacting particles moving in a d-dimensional billiard is considered here. A suitable coordinate transformation leads to the problem of a particle in an unconventional hyperbilliard. A dynamical map can be readily…

A discussion on the momentum evolution of an impurity interacting via a finite delta potential repulsion with a non-interacting fermionic background gas is presented. It has recently been shown that the momentum evolution of this system…

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…