Stadium billiard with moving walls

Abstract

We study the evolution of the energy distribution for a stadium with moving walls. We consider one period driving cycle, which is characterized by an amplitude A and wall velocity V . This evolving energy distribution has both "parametric" and "stochastic" components. The latter are important for the theory of quantum irreversibility and dissipation in driven mesoscopic devices (eg in the context of quantum computation). For extremely slow wall velocity V the spreading mechanism is dominated by transitions between neighboring levels, while for larger (non-adiabatic) velocities the spreading mechanism has both perturbative and non-perturbative features. We present, for the first time, a numerical study which is aimed in identifying the latter features. A procedure is developed for the determination of the various V regimes. The possible implications on linear response theory are discussed.

Robust Exponential Acceleration in Time-Dependent Billiards

“…Fermi proposed such a model for explaining the origin of cosmic rays [3]. Similar models appear in studies of capacitive discharges in plasmas [4], nuclear fission [5], and mesoscopic devices [6]. In these models the billiard boundary may move randomly or in a smooth fashion-hereafter we consider the smooth case.…”

Loschmidt echo and the local density of states

“…So, it is a good measure of the perturbation action over the system. This quantity can be measured in different ways [27]. In our case, we take the half distance around the mean value that contains the 70% of the probability [27].…”

“…This quantity can be measured in different ways [27]. In our case, we take the half distance around the mean value that contains the 70% of the probability [27]. We compute the width σ for both perturbations introduced before (see Fig.1).…”

Resonant population transfer in the time-dependent quantum elliptical billiard

“…Recently, the dynamical properties of classical time-dependent two-dimensional billiards have attracted major attention, especially in the context of Fermi acceleration [1,2,3,4,5,6,7,8], which is defined as the unbounded energy gain of an ensemble of particles exposed to some external driving force [9]. Concerning the quantum dynamics of time-dependent billiards, there exist several studies investigating the quantum version of the one-dimensional Fermi-Ulam model (or variants of it) [10,11,12,13,14,15,16,17,18,19,20,21], but, to our knowledge, only two studies [22,23] investigate time-dependent billiards in higher dimensions.…”

“…Concerning higher dimensional billiards, the one-pulse response of a twodimensional stadium billiard to a deformation of the boundary has been studied [23] by analyzing the evolving energy distribution. For small wall velocities, the spreading mechanism of this distribution is dominated by transitions between neighboring levels, while this is not the case for non-adiabatic wall velocities.…”