Transmission and reflection in the stadium billiard: Time-dependent asymmetric transport

The survival probability of the open stadium billiard with one hole on its boundary is well known to decay asymptotically as a power law. We investigate the transmission and reflection survival probabilities for the case of two holes placed asymmetrically. Classically, these distributions are shown to lose their algebraic decay tails depending on the choice of injecting hole, therefore exhibiting asymmetric transport. The mechanism behind this is explained while exact expressions are given and confirmed numerically. We propose a model for experimental observation of this effect using semiconductor nanostructures and comment on the relevant quantum time scales.