Nonequilibrium Casimir pressure for two graphene-coated plates: Quantum field theoretical approach

We consider the nonequilibrium Casimir pressure in the system of two parallel graphene-coated plates one of which is either warmer or cooler than the environment. The electromagnetic response of graphene coating characterized by the nonzero energy gap and chemical potential is described in the framework of the Dirac model by means of the polarization tensor. It is shown that the magnitude of the nonequilibrium Casimir pressure on a warmer plate than the environment is larger and on a cooler plate is smaller than the magnitude of the standard Casimir pressure in the state of thermal equilibrium. According to our results, the spatially local theory underestimates the role of the effects of nonequilibrium. This underestimation increases for asmaller chemical potential of the graphene coating and at lower temperatures of the cooled plate. Possible applications of the obtained results are discussed.