Quantum chaos in a harmonic waveguide with scatterers

TL;DR

This paper investigates how adding scatterers to a harmonic waveguide induces quantum chaos, enabling the study of the transition from integrability to chaos through computationally efficient methods, and confirming chaos via spectral and eigenstate analysis.

Contribution

It introduces a model with zero-range scatterers in a harmonic waveguide that allows efficient computation of eigenstates and explores the quantum chaos transition as scatterer number and strength increase.

Findings

Eigenstate thermalization occurs at 32 scatterers.

Spectral properties indicate transition to quantum chaos.

Eigenstates become more delocalized with increasing scatterers.

Abstract

A set of zero-range scatterers along its axis lifts the integrability of a harmonic waveguide. Effective solution of the Schr\"odinger equation for this model is possible due to the separable nature of the scatterers and millions of eigenstates can be calculated using modest computational resources. Integrability-chaos transition can be explored as the model chaoticity increases with the number of scatterers and their strengths. The regime of complete quantum chaos and eigenstate thermalization can be approached with 32 scatterers. This is confirmed by properties of energy spectra, the inverse participation ratio, and fluctuations of observable expectation values.