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 $ϕ^4$ theory with an arbitrary time dependent interaction parameter $λ(t)=λf(ω_0 t)$, where $ω_0$ is the drive frequency and derive the RG equations for the system using a Keldysh diagrammatic technique. We show that the scaling of $ω_0$ 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 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 motions of the bosons and discuss their significance for systems near critical points described by time-dependent Landau-Ginzburg theories.

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