The Onset of Chaos in the Quantum Hard-Sphere Gas

TL;DR

This paper establishes the condition under which a dilute quantum hard-sphere gas exhibits quantum chaos, linking the particle wavelength and mean free path, with implications for fermionic systems and their energy states.

Contribution

It introduces a specific criterion, λ ≪ ℓ, for the onset of quantum chaos in dilute hard-sphere gases, including all energy states for fermions.

Findings

Quantum chaos occurs when λ ≪ ℓ.

All energy eigenstates are chaotic for fermions with λ_F ≪ ℓ.

Physical implications of chaos in quantum gases are discussed.

Abstract

We show that the condition for the appearance of quantum chaos (Wigner-Dyson distribution of energy eigenvalues, gaussian-random energy eigenfunctions) in a dilute gas of many hard spheres is $\lambda \ll \ell$, where $\lambda$ is the wavelength of a typical particle and $\ell$ is the mean free path between collisions. For fermions with Fermi wavelength $\lambda_F \ll \ell$, this implies that all energy eigenstates, including the ground state, are chaotic. Physical implications are discussed.