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The Trace Formula and Spectral Statistics: Beyond the Diagonal Approximation
Keating, J.P.; Bogomolny, E.B
HPLBRIMS9614
Keyword(s): spectral statistics; quantum chaos; random matrix theory
Abstract: We calculate the 2point spectral correlation function for classically chaotic systems in the semiclassical limit using Gutzwiller's trace formula. The offdiagonal contributions from pairs of nonidentical periodic orbits are evaluated by relating them to the diagonal terms. The behaviour we find is similar to that recently discovered to hold for disordered systems using nonperturbative supersymmetric methods. Our analysis generalizes immediately to include parametric statistics, higherorder correlations, and to the study of the semiclassical distribution of matrix elements.
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