  The connection of a superconductor to a chaotic ballistic quantum dot leads
to interesting phenomena, most notably the appearance of a hard gap in its
excitation spectrum. Here we treat such an Andreev billiard semiclassically
where the density of states is expressed in terms of the classical trajectories
of electrons (and holes) that leave and return to the superconductor. We show
how classical orbit correlations lead to the formation of the hard gap, as
predicted by random matrix theory in the limit of negligible Ehrenfest time
$\tE$, and how the influence of a finite $\tE$ causes the gap to shrink.
Furthermore, for intermediate $\tE$ we predict a second gap below $E=\pi\hbar
/2\tE$ which would presumably be the clearest signature yet of $\tE$-effects.
