UNIVERSAL LEVEL STATISTICS IN THE PRESENCE OF ANDREEV SCATTERING

We study the spectral eigenvalue statistics of tight-binding random ma trix ensembles in the presence of Andreev scattering (As). The nearest -level spacing distribution function is shown to follow a distribution P-AS(s) which is distinct from the three well known Wigner-Dyson clas ses describing disordered 'normal' conductors. Numerical results for P -AS(s) are Obtained for a three-dimensional random tight-binding Hamil tonian and also for a two-dimensional transmission matrix, both includ ing Andreev scattering. The P-AS(s) distribution is also analytically reproduced and is shown to coincide with that obtained by folding a GO E metallic spectrum around E = 0.