Wave Function Scarring in Open Ballistic Quantum Dots

Abstract

Numerical simulations of the quantum mechanical transport and corresponding wave functions of open quantum dots, with leads supporting a small number of propagating modes, have been carried out. We have found that the wave functions that coincide with some of the resonance features in the transport appear to show scarring, that is, the amplitude of the wave functions are highly concentrated along underlying single, classical trajectories. We discuss some of the conditions necessary for dot shape and size and the magnetic field for this scarring effect to become apparent. In particular, we find the nature of the leads to be quite important, with injection of the electrons via an angled, collimated beam being crucial for the excitation of a preferred set of regular, semiclassical trajectories.