We consider the effect of spin-orbit coupling on the low energy excitation
spectrum of an Andreev billiard (a quantum dot weakly coupled to a
superconductor), using a dynamical numerical model (the spin Andreev map).
Three effects of spin-orbit coupling are obtained in our simulations: In zero
magnetic field: (1) the narrowing of the distribution of the excitation gap;
(2) the appearance of oscillations in the average density of states. In strong
magnetic field: (3) the appearance of a peak in the average density of states
at zero energy. All three effects have been predicted by random-matrix theory.Comment: 5 pages, 4 figure