Spectral properties of quantum $N$-body systems versus chaotic properties of their mean field approximations

TL;DR

This paper provides numerical evidence of a correspondence between the spectral properties of quantum bosonic systems and the chaotic behavior of their mean field approximations, linking quantum spectra to classical chaos.

Contribution

It demonstrates a novel quantum-classical correspondence in bosonic systems, connecting quantum spectral features with mean field dynamical chaos.

Findings

Spectral properties of quantum Hamiltonian relate to mean field chaos.

Numerical evidence supports quantum-classical correspondence.

Discusses limits of infinite density and thermodynamic limit.

Abstract

We present numerical evidence that in a system of interacting bosons there exists a correspondence between the spectral properties of the exact quantum Hamiltonian and the dynamical chaos of the associated mean field evolution. This correspondence, analogous to the usual quantum-classical correspondence, is related to the formal parallel between the second quantization of the mean field, which generates the exact dynamics of the quantum $N$-body system, and the first quantization of classical canonical coordinates. The limit of infinite density and the thermodynamic limit are then briefly discussed.