Semiclassical approach to matrix energy correlations and time delay in chaotic systems
arXiv:2202.08609 · doi:10.1103/PhysRevE.105.044213
Abstract
The -dimensional scattering matrix which connects incoming to outgoing waves in a chaotic systyem is always unitary, but shows complicated dependence on the energy. This is partly encoded in correlators constructed from traces of powers of , averaged over , and by the statistical properties of the time delay operator, . Using a semiclassical approach for systems with broken time reversal symmetry, we derive two kind of expressions for the energy correlators: one as a power series in whose coefficients are rational functions of , and another as a power series in whose coefficients are rational functions of . From the latter we extract an explicit formula for which is valid for all and is in agreement with random matrix theory predictions.
arXiv comment6 pages
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