Parametric Excitation of a 1D Gas in Integrable and Nonintegrable Cases

TL;DR

This paper investigates how a 1D gas's response to periodic coupling modulation varies between integrable and nonintegrable models, revealing a potential experimental method to distinguish these regimes based on excitation sensitivity.

Contribution

It provides a detailed analysis of the dynamic structure factors in 1D gases, highlighting the differing low-frequency responses in integrable versus nonintegrable cases and proposing an experimental probe for integrability.

Findings

Nonintegrable systems respond to very low-frequency excitations near the mean level spacing.

Integrable systems require much higher excitation frequencies to be significantly affected.

The difference in response can be used to experimentally identify integrability in 1D gases.

Abstract

We study the response of a highly excited 1D gas with pointlike interactions to a periodic modulation of the coupling constant. We calculate the corresponding dynamic structure factors and show that their low-frequency behavior differs dramatically for integrable and nonintegrable models. Nonintegrable systems are sensitive to excitations with frequencies as low as the mean level spacing, whereas much higher frequencies are required to excite an integrable system. This effect can be used as a probe of integrability for mesoscopic 1D systems and can be observed experimentally by measuring the heating rate of a parametrically excited gas.