Semiclassics of Andreev billiards
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By coupling a superconductor to a quantum cavity or dot one may decide whether its classical counterpart has integrable or chaotic dynamics by looking at the density of states. Random matrix theory (RMT) predicts a true gap of the order of the Thoules energy ET if the classical motion is chaotic and an exponential damping in the case of integrable motion. We use semiclassical techniques developed in the recent years to reproduce the RMT predictions. Using the same techniques we show that the existance of a superconductor in proximity of the dot has crucial effects on the conductance.
