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.New approach to periodic orbit theory of spectral correlations

Towards a semiclassical understanding of chaotic single- and many-particle quantum dynamics at post-Heisenberg time scales

“…The form factor for τ > 1 was then formally obtained in a way that was inspired by a diagrammatic expansion of a four-point correlation function of spectral determinants around a second saddle point of the corresponding field theory [19]. Later on this procedure was connected to the use of the Riemann Siegel lookalike formula for the spectral determinant [20] and to analytic continuation [21]. All such approaches have in common that they extend semiclassical results for τ < 1 to the regime τ > 1 by additionally invoking quantum mechanical unitarity in one or the other way.…”