Distribution of multiple avoided crossings: numerical evaluation

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Abstract
The authors compute numerically the distribution rho ( Delta in ) of Delta in , the local minimum distance (avoided crossing gap size) between neighbouring energy levels of two model systems. They find that limit Delta in to 0 rho approximately Delta in . The result differs from that expected for a GOE model, for which Wilkinson (1988) has shown that in the small Delta in limit rho ( Delta in ) is constant. They suggest that the discrepancy arises from parametric correlations which are known to exist but are absent from the GOE.

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