Mode coupling induced dissipative and thermal effects at long times after a quantum quench

TL;DR

This paper investigates how mode coupling from a periodic potential affects the long-time behavior of a Luttinger liquid after a quantum quench, revealing induced dissipation and thermal effects in the out-of-equilibrium steady state.

Contribution

It demonstrates that an irrelevant periodic potential in equilibrium can induce dissipation and thermalization in the non-equilibrium steady state of a quenched Luttinger liquid.

Findings

Periodic potential generates a finite temperature in the steady state.

Mode coupling leads to dissipation and finite lifetime of bosonic modes.

Even irrelevant perturbations can have significant effects out of equilibrium.

Abstract

An interaction quench in a Luttinger liquid can drive it into an athermal steady state. We analyze the effects on such an out of equilibrium state of a mode coupling term due to a periodic potential. Employing a perturbative renormalization group approach we show that even when the periodic potential is an irrelevant perturbation in equilibrium, it has important consequences on the athermal steady state as it generates a temperature as well as a dissipation and hence a finite life-time for the bosonic modes.