Classical foundations of many-particle quantum chaos

TL;DR

This paper extends semiclassical theory of quantum chaos to many-particle systems with local interactions, revealing new partner orbit mechanisms crucial for understanding their spectral properties.

Contribution

It introduces a novel correlation mechanism for periodic orbits in many-particle chaotic systems, expanding the scope of semiclassical analysis beyond low-dimensional cases.

Findings

Discovery of new partner orbits specific to many-particle systems

Demonstration that these partner orbits dominate in large N systems

Establishment of their importance for a consistent semiclassical theory

Abstract

In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however, the scope of this approach has been mainly limited to systems of a few particles with low-dimensional phase spaces. In the present work we consider N-particle chaotic systems with local homogeneous interactions, where N is not necessarily small. Based on a model of coupled cat maps we demonstrate emergence of a new mechanism for correlation between periodic orbit actions. In particular, we show the existence of partner orbits which are specific to many-particle systems. For a sufficiently large N these new partners dominate the spectrum of correlating periodic orbits and seem to be necessary for construction of a consistent many-particle semiclassical theory.