Many-Particle Quantum Chaos Beyond the Ehrenfest "Number"

Abstract

The theory of quantum chaos demonstrates the effectiveness of semiclassical methods based on periodic-orbit correlations for calculating spectral correlations in single-particle systems. However, extending this approach to the many-particle chaotic models is non-trivial. The development of a dedicated theory in the thermodynamic-semiclassical limit, where both the number of particles and 1/ћ tend to infinity, is required. In this paper, we address the above problem for a chain of cat maps with local nearest-neighbor interaction. We study the correlation mechanism between classical periodic orbits, which becomes relevant in the thermodynamic-semiclassical limit. Our findings are supported by exact results and by numerical evidence obtained for the coupled cat map model.