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Physical Review A

Improving wave-packet revivals in circular billiards by applying constant magnetic fields

Guilherme Jurkevicz Delben, André Gusso, M. G. E. da Luz

Published May 31, 2006• 1 citation
Publisher

Abstract

We show that the revivals structure of Gaussian wave packets for a charged particle with nonzero linear momentum placed in a circular billiard can be considerably improved by applying a perpendicular constant magnetic field of correct chosen intensity. To obtain the desired enhancement, the field must be turned on only at certain time values. We also briefly investigate how the shape of the evoluted packet at the revivals, with and without an external $B$, compares with the initial state.

DOI
10.1103/physreva.73.055601

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We show that the revivals structure of Gaussian wave packets for a charged particle with nonzero linear momentum placed in a circular billiard can be considerably improved by applying a perpendicular constant magnetic field of correct chosen intensity. To obtain the desired enhancement, the field must be turned on only at certain time values. We also briefly investigate how the shape of the evoluted packet at the revivals, with and without an external BBB, compares with the initial state.
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A Gaussian wave packet confined to move on a plane perpendicular to a magnetic field remains a Gaussian wave packet in its time evolution. The average position and momentum follow the Ehrenfest equations which are identical to the classical Hamilton equations. A set of nonlinear equations decoupled from the Ehrenfest equation is derived for the parameters describing the time evolution of the density distribution and phases of a wave packet. Explicit solutions are then obtained when the “internal” angular momentum of the wave packet vanishes. In this case it is shown that the motion of the wave packet is a superposition of a translational motion, a rotation and a vibration.