Mode-Coupling-Induced Dissipative and Thermal Effects at Long Times after a Quantum Quench

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 lifetime for the bosonic modes.