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.

Figure 1

$C^K(q=0.5,\omega )$ and $2\mathrm{Im}[C^R(q=0.5,\omega )]$ in equilibrium $K_{\mathrm{eq}}=K_{\mathrm{neq}}=2.0$ and after a quench $K_{\mathrm{eq}}=2$, $K_{\mathrm{neq}}=3$.

Figure 2

Strength of the dissipation $\eta$ for $K_0=3$, $\gamma =2$ and $g=0.05$ and $g=0.1$.