Evolution of wave-function statistics from closed quantum billiards up to the open quantum dot limit: Application to the measurement of dynamical properties through imaging experiments

Abstract

We discuss the evolution of the electronic and scattering properties of a square billiard connected to the outside either by tunneling barriers or by progressively higher-conductance leads. The slightest connection already induces features of chaotic dynamics in the otherwise regular system. In the absence of large ensembles for energy level statistics or power spectrum analysis, we propose the distribution of the local densities to inspect the character of the underlying dynamics of a scattering state. We show that the wave-function statistics in wide open chaotic billiards strongly deviates from available predictions. The precursors of scarred wave functions are found in wave-function vortices that are tuned by the lead width.