相关论文: Bounded Gain of Energy on the Breathing Circle Bil…

We study billiard dynamics inside an ellipse for which the axes lengths are changed periodically in time and an $O(\delta)$-small quartic polynomial deformation is added to the boundary. In this situation the energy of the particle in the…

We perform the first long-time exploration of the classical dynamics of a driven billiard with a four dimensional phase space. With increasing velocity of the ensemble we observe an evolution from a large chaotic sea with stickiness due to…

The quantum dynamics of a chaotic billiard with moving boundary is considered in this work. We found a shape parameter Hamiltonian expansion which enables us to obtain the spectrum of the deformed billiard for deformations so large as the…

The periodic Lorentz gas with external field and iso-kinetic thermostat is equivalent, by conformal transformation, to a billiard with expanding phase-space and slightly distorted scatterers, for which the trajectories are straight lines. A…

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…

Some dynamical properties of time-dependent driven elliptical-shaped billiard are studied. It was shown that for the conservative time-dependent dynamics the model exhibits the Fermi acceleration [Phys. Rev. Lett. 100, 014103 (2008)]. On…

We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards…

The dynamics of a time-dependent stadium-like billiard are studied by a four dimensional nonlinear mapping. We have shown that even without any dissipation, the particle experiences a decrease on its velocity. Such condition is related with…

We study the energy dynamics of a particle in a billiard subject to a rapid periodic drive. In the regime of large driving frequencies $\omega$, we find that the particle's energy evolves diffusively, which suggests that the particle's…

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…

A competition between decay and growth of energy in a time-dependent stadium billiard is discussed giving emphasis in the decay of energy mechanism. A critical resonance velocity is identified for causing of separation between ensembles of…

We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a `piston', i.e. a line-segment, which moves back and forth along a…

The changeover from normal to super diffusion in time dependent billiards is explained analytically. The unlimited energy growth for an ensemble of bouncing particles in time dependent billiards is obtained by means of a two dimensional…

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although…

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…

We present a semiclassical theory for the excitation spectrum of a ballistic quantum dot weakly coupled to a superconductor, for the generic situation that the classical motion gives rise to a phase space containing islands of regularity in…

Statistical equilibration of energies in a slow-fast system is a fundamental open problem in physics. In a recent paper, it was shown that the equilibration rate in a springy billiard can remain strictly positive in the limit of vanishing…

Can elliptic islands contribute to sustained energy growth as parameters of a Hamiltonian system slowly vary with time? In this paper we show that a mushroom billiard with a periodically oscillating boundary accelerates the particle inside…

We present a dynamical analysis of a classical billiard chain -- a channel with parallel semi-circular walls, which can serve as a model for a bended optical fiber. An interesting feature of this model is the fact that the phase space…

We consider the three-dimensional dynamics of systems of many interacting hard spheres, each individually confined to a dispersive environment, and show that the macroscopic limit of such systems is characterized by a coefficient of heat…