New approach to periodic orbit theory of spectral correlations

Abstract

The existing periodic orbit theory of spectral correlations for classically chaotic systems relies on the Riemann-Siegel-like representation of the spectral determinants which is still largely hypothetical. We suggest a simpler derivation using analytic continuation of the periodic-orbit expansion of the pertinent generating function from the convergence border to physically important real values of its arguments. As examples we consider chaotic systems without time reversal as well as the Riemann zeta function and Dirichlet L-functions zeros.

arXiv comment15 pages, 2 figures

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Cited by in corpus (2)

• Using Lagrangian descriptors to calculate the Maslov index of periodic orbits
• Towards a semiclassical understanding of chaotic single- and many-particle quantum dynamics at post-Heisenberg time scales