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A perturbative renormalization group approach is employed to study the effectof a periodic potential on a system of one-dimensional bosons in anon-equilibrium steady-state due to an initial interaction quench. Therenormalization group flows are modified significantly from the well knownequilibrium Berezinski-Kosterlitz-Thouless form. They show several new featuressuch as, a generation of an effective temperature, generation of dissipation,as well as a change in the location of the quantum critical point separatingthe weak coupling and strong coupling phases. Detailed results on theweak-coupling side of the phase diagram are presented, such as therenormalization of the parameters and the asymptotic behavior of thecorrelation functions. The physical origin of the generated temperature andfriction is discussed.

Thermalization and dissipation in out of equilibrium quantum systems: A perturbative renormalization group approach