HP Labs Technical Reports

The Trace Formula and Spectral Statistics: Beyond the Diagonal Approximation

Keating, J.P.; Bogomolny, E.B

HPL-BRIMS-96-14

Keyword(s): spectral statistics; quantum chaos; random matrix theory

Abstract: We calculate the 2-point spectral correlation function for classically chaotic systems in the semiclassical limit using Gutzwiller's trace formula. The off-diagonal contributions from pairs of non-identical 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 non-perturbative supersymmetric methods. Our analysis generalizes immediately to include parametric statistics, higher-order correlations, and to the study of the semiclassical distribution of matrix elements.

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