An eccentrically perturbed Tonks-Girardeau gas

TL;DR

This paper analytically studies a Tonks-Girardeau gas in a harmonic trap with an eccentric delta perturbation, analyzing static properties and dynamic evolution, revealing collapse and revival phenomena akin to the Talbot effect.

Contribution

It provides an exact eigensolution for the single-particle problem with eccentric perturbation and explores the resulting static and dynamic properties of the many-body gas.

Findings

The density and energy profiles depend on perturbation strength and position.

The gas exhibits collapse and revival dynamics after perturbation removal.

The behavior shows similarities to the Talbot effect in optics.

Abstract

We investigate the static and dynamic properties of a Tonks-Girardeau gas in a harmonic trap with an eccentric $\delta$-perturbation of variable strength. For this we first find the analytic eigensolution of the single particle problem and use this solution to calculate the spatial density and energy profiles of the many particle gas as a function of the strength and position of the perturbation. We find that the crystal nature of the Tonks state is reflected in both the lowest occupation number and momentum distribution of the gas. As a novel application of our model, we study the time evolution of the the spatial density after a sudden removal of the perturbation. The dynamics exhibits collapses and revivals of the original density distribution which occur in units of the trap frequency. This is reminiscent of the Talbot effect from classical optics.