Excitation energy after a smooth quench in a Luttinger liquid

TL;DR

This paper investigates how the excitation energy in a Luttinger liquid decays with quench time during smooth parameter changes, revealing universal power-law behaviors at zero and finite temperatures.

Contribution

It provides a theoretical analysis of excitation energy decay in Luttinger liquids during smooth quenches, establishing universal power-law exponents.

Findings

Excitation energy decays as an inverse power of quench time.

Universal exponents are -2 at zero temperature and -1 at finite temperature.

The analysis applies within the low energy LL validity range.

Abstract

Low energy physics of quasi-one-dimensional ultracold atomic gases is often described by a gapless Luttinger liquid (LL). It is nowadays routine to manipulate these systems by changing their parameters in time but, no matter how slow the manipulation is, it must excite a gapless system. We study a smooth change of parameters of the LL (a smooth "quench") with a variable quench time and find that the excitation energy decays with an inverse power of the quench time. This universal exponent is -2 at zero temperature, and -1 for slow enough quenches at finite temperature. The smooth quench does not excite beyond the range of validity of the low energy LL description.