Transmission and Reflection in the Stadium Billiard: Time-dependent asymmetric transport

TL;DR

This paper studies how particles transmit and reflect in a chaotic stadium billiard with asymmetrically placed holes, providing new classical decay expressions and proposing a quantum experimental model.

Contribution

It introduces exact classical expressions for survival probabilities in asymmetric stadium billiards and suggests a quantum experimental setup for observing asymmetric transport.

Findings

Classical survival probabilities decay algebraically or exponentially.

Exact expressions for decay rates are derived and numerically confirmed.

A quantum model for experimental observation is proposed.

Abstract

We investigate the transmission and reflection survival probabilities for the chaotic stadium billiard with two holes placed asymmetrically. Classically, these distributions are shown to have algebraic or exponential decays depending on the choice of injecting hole and exact expressions are given for the first time and confirmed numerically. As there is no reported quantum theoretical or experimental analogue we propose a model for experimental observation of the asymmetric transport using semiconductor nano-structures and comment on the relevant quantum time-scales.