Persistent Currents in Quantum Chaotic Systems

TL;DR

This paper derives semiclassical formulas for persistent currents in chaotic billiards, showing they are smaller than in integrable systems, thus providing a way to experimentally identify quantum signatures of classical chaos.

Contribution

It introduces new semiclassical formulas for persistent currents in chaotic billiards and compares them to integrable systems, highlighting their potential as experimental signatures.

Findings

Persistent currents in chaotic billiards are significantly smaller than in integrable systems.

Derived semiclassical formulas for typical and average persistent currents.

Persistent currents can serve as experimental indicators of quantum chaos.

Abstract

The persistent current of ballistic chaotic billiards is considered with the help of the Gutzwiller trace formula. We derive the semiclassical formula of a typical persistent current $I^{typ}$ for a single billiard and an average persistent current $<I>$ for an ensemble of billiards at finite temperature. These formulas are used to show that the persistent current for chaotic billiards is much smaller than that for integrable ones. The persistent currents in the ballistic regime therefore become an experimental tool to search for the quantum signature of classical chaotic and regular dynamics.