Time-dependent Robin boundary conditions in the dynamical Casimir effect
  Motivated by experiments in which moving boundaries are simulated by time-dependent properties of static systems, we discuss the model of a massless scalar field submitted to a time-dependent Robin boundary condition (BC) at a static mirror in 1+1 dimensions. Using a perturbative approach, we compute the spectral distribution of the created particles and the total particle creation rate, considering a thermal state as the initial field state. 
C. Farina, Hector O. Silva, Andreson L. C. Rego and Danilo T. Alves
quant-ph hep-th