Quantum and classical chaos of a two-electron system in a quantum wire

TL;DR

This paper explores the relationship between classical and quantum chaos in a two-electron quantum wire system, introducing a new measure of chaos and analyzing energy level statistics to reveal underlying scaling properties.

Contribution

It presents a novel classical chaos measure and demonstrates its connection to quantum energy level statistics, highlighting quantum-classical correspondence in a two-electron system.

Findings

Classical dynamics exhibit scaling properties absent in quantum dynamics.

A new type of Lyapunov exponent effectively measures chaos in this system.

Energy level statistics align with classical chaos indicators, supporting quantum-classical correspondence.

Abstract

We study classical and quantum dynamics of two spinless particles confined in a quantum wire with repulsive or attractive Coulomb interaction. The interaction induces irregular dynamics in classical mechanics, which reflects on the quantum properties of the system in the energy level statistics (the signatures of quantum chaos). We investigate especially closer correspondence between the classical and quantum chaos. The present classical dynamics has some scaling property, which the quantum counterpart does not have. However, we demonstrate that the energy level statistics implies the existence of the corresponding scaling property even in the quantum system. Instead of ordinary maximum Lyapunov exponent (MLE), we introduce a novel kind of MLE, which is shown to be suitable measure of chaotic irregularity for the present classical system. We show that tendency of the energy dependence of the Brody parameter, which characterizes the energy level statistics in the quantum system, is consistent with that of the novel kind of MLE.