  Recently semiclassical approximations have been successfully applied to study
the effect of a superconducting lead on the density of states and conductance
in ballistic billiards. However, the summation over classical trajectories
involved in such theories was carried out using the intuitive picture of
Andreev reflection rather than the semiclassical reasoning. We propose a method
to calculate the semiclassical sums which allows us to go beyond the diagonal
approximation in these problems. In particular, we address the question of
whether the off-diagonal corrections could explain the gap in the density of
states of a chaotic Andreev billiard.
