Correlations in the actions of periodic orbits derived from quantum chaos
Abstract
We discuss twopoint correlations of the actions of classical periodic orbits in chaotic systems. For systems where the semiclassical trace formula is exact and the spectral statistics follow random matrix theory, there exist nontrivial correlations between actions, which we express in a universal form. We illustrate this result with the analogous problem of the pair correlations between prime numbers. We also report on numerical studies of three chaotic systems where the semiclassical trace formula is only approximate, but nevertheless these unexpected action correlations are observed.
 Publication:

Physical Review Letters
 Pub Date:
 December 1993
 DOI:
 10.1103/PhysRevLett.71.4326
 Bibcode:
 1993PhRvL..71.4326A
 Keywords:

 05.45.+b;
 03.65.Sq;
 Semiclassical theories and applications