Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard

A semiclassical theory is developed for the appearance of an excitation gap in a ballistic chaotic cavity connected by a point contact to a superconductor. Diffraction at the point contact is a singular perturbation in the limit (h) over bar -->0, which opens up a gap E-gap in the excitation spectrum. The time scale (h) over bar /E(gap)proportional toalpha(-1)lnh (with alpha the Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of quantum chaos.