Quantum localization due to mirror plane symmetry

Abstract

With suitably directed initial states, we show how the time-averaged density of an evolving wave packet localizes on a mirror plane. A classical analog of this behavior can sometimes be found with trajectories weighted according to a Wigner distribution of the initial quantum state. However, in the limit of strongly chaotic classical dynamics, no such classical analog exists and the quantum localization in the density tends to be stronger by a factor of 2. Two very different systems are used to illustrate this effect, one being a three-dimensional model for a lithium atom moving within a ${\text{C}}_{60}$ cage and the other being a two-dimensional double well problem.