  When coupling a superconductor to a normal conducting region the physical
properties of the system are highly affected by the superconductor. We will
investigate the effect of one or two superconductors on the conductance of a
ballistic chaotic quantum dot to leading order in the total channel number
using trajectory based semiclassics. The results show that the effect of one
superconductor on the conductance is of the order of the number of channels and
that the sign of the correction from the Drude conductance depends on the
particular ratios of the numbers of channels of the superconducting and normal
conducting leads. In the case of two superconductors with the same chemical
potential we will also see how the conductance and the sign of quantum
corrections are affected by their phase difference. As far as random matrix
theory results exist these are reproduced by our calculations. Furthermore in
the case that the chemical potential of the superconductors is the same as that
of one of the two normal leads the conductance shows, under certain conditions,
similar effects as a normal metal-superconductor junction. The semiclassical
framework is also able to treat the thermopower of chaotic Andreev billiards
consisting of one chaotic dot, two normal leads and two superconducting islands
and shows it to be antisymmetric in the phase difference of the
superconductors.
