Chaotic Signatures in the Spectrum of a Quantum Double Well

TL;DR

This paper investigates the spectral properties of a quantum double well with a square barrier, revealing signs of quantum chaos through level statistics that resemble Wigner distributions, especially under ensemble averaging.

Contribution

It demonstrates the emergence of Wigner-like level statistics in a quantum double well system and explores how ensemble averaging enhances this chaotic signature.

Findings

Level statistics indicate quantum chaos near the barrier.

Ensemble averaging improves Wigner distribution correspondence.

Spectral signatures suggest adiabatic modulation effects.

Abstract

The spectrum of a double well constructed of a square barrier embedded in an infinite well is analyzed. Level statistics for levels slightly above the barrier show signs of Wigner statistics usually associated with quantum chaos. The correspondence with Wigner statistics improves when an ensemble of systems with slightly different barrier heights is taken, possibly reflecting an adiabatic time-dependent modulation of the barrier.