A perturbative renormalization group approach to driven quantum systems.

We use a perturbative momentum shell renormalization group (RG) approach to study the properties of a driven quantum system at zero temperature. To illustrate the technique, we consider a bosonic 4 theory with an arbitrary time dependent interaction parameter λ(t) = λ f(ω0t), where ω0 is the drive frequency and we derive the RG equations for the system using a Keldysh diagrammatic technique. We show that the scaling of ω0 is analogous to that of temperature for a system in thermal equilibrium and its presence provides a cutoff scale for the RG flow. We analyze the resultant RG equations, derive an analytical condition for such a drive to take the system out of the gaussian regime, and show that the onset of the non-gaussian regime occurs concomitantly with the appearance of non-perturbative mode coupling terms in the effective action of the system. We supplement the above-mentioned results by obtaining them from equations of motion of the bosons and discuss their significance for systems near critical points described by time-dependent Landau-Ginzburg theories.