Transport of a wave packet via an open quantum dot: on the correspondence with classical billiards

The evolution of two-dimensional Gaussian wave packets in mesoscopic dots was analyzed by solving the time-dependent Schrödinger equation numerically. It was found that the motion of the probability density peaks relates to the classical orbits of billiards. The effect of the dot shape (circle, ellipse or stadium) on the time evolution of the wave packet is discussed in terms of the symmetry of the eigenfunctions.