Wave Packet Dynamics in Driven Circular and Elliptical Billiards

Abstract

We develop an approach to find the eigen functions of two dimensional time dependent circular billiard in the presence of external modulating force. Here, we calculate revival and fractional-revival times for the driven circular billiard and show that they are unique but not symmetric. We analyzed the time dependent population and energy of different eigenstates. Also this thesis describes a numerical method to propagate a random initial state in time dependent elliptical billiard analyzed by time dependent boundary conditions. In this method we made multiple variables transformation to remove the time dependency of boundary conditions. Similarly expansion of wave function in a suitable basis results time dependent large system of coupled differential equations are obtained, that can be solved by standard techniques. We than examine the time evolution of eigenstates energies in driven elliptical billiard. The energy a function of applied driving frequency shows a series of resonances. At these resonances the population of eigen states vary periodically with a period Tb. The resonances occurs, when the driving frequency matches the mean energetic difference of involved states