Keldysh approach to periodically driven systems with a fermionic bath:   non-equilibrium steady state, proximity effect and dissipation
  We study properties of a periodically driven system coupled to a thermal bath. As a nontrivial example, we consider periodically driven metallic system coupled to a superconducting bath. The effect of the superconductor on the driven system is two-fold: it (a) modifies density of states in the metal via the proximity effect and (b) acts as a thermal bath for light-excited quasi-particles. Using Keldysh formalism, we calculate, nonpertubatively in the system-bath coupling, the steady-state properties of the system and obtain non-equilibrium distribution function. The latter allows one to calculate observable quantities which can be spectroscopically measured in tunneling experiments. 
Dong E. Liu, Alex Levchenko, and Roman M. Lutchyn
cond-mat.supr-con cond-mat.mes-hall