DISTRIBUTION OF MULTIPLE AVOIDED CROSSINGS - NUMERICAL EVALUATION

We compute numerically the distribution rho-(DELTA-epsilon) of DELTA-epsilon, the local minimum distance (avoided crossing gap size) between neighbouring energy levels of two model systems. We find that lim-DELTA-epsilon --> 0 rho approximately DELTA-epsilon. The result differs from that expected for a GOE model, for which Wilkinson has shown that in the small DELTA-epsilon limit rho-(DELTA-epsilon) is constant. We suggest that the discrepancy arises from parametric correlations which are known to exist but are absent from the GOE.