Periodic orbit action correlations in the Baker map

Abstract

Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the existence of universal periodic orbit correlations. The calculation of periodic orbit sums for the Baker map can be performed with the help of a Perron-Frobenius-type operator. This makes it possible to study periodic orbit correlations for orbits with period up to 500 iterations of the map. Periodic orbit correlations are found to agree quantitatively with the predictions from random matrix theory up to a critical length determined by the semiclassical error. Exponentially increasing terms dominate the correlations for longer orbits which are due to the violation of unitarity in the semiclassical approximation.