New approach to periodic orbit theory of spectral correlations

TL;DR

This paper introduces a simplified method for deriving spectral correlations in chaotic systems by analytically continuing the generating function, with applications to Riemann zeta and L-functions.

Contribution

It proposes a new approach using analytic continuation to improve the periodic orbit theory of spectral correlations, avoiding reliance on hypothetical representations.

Findings

Successful derivation for systems without time reversal

Application to zeros of Riemann zeta and Dirichlet L-functions

Simpler and more direct theoretical framework

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.