Parametric down conversion of a bosonic thermofield vacuum
  We consider a process of parametric down conversion where the input state is a bosonic thermofield vacuum. This state leads to a parametric down conversion, generating an output of two excited photons. Following a thermofield dynamics scheme, the input state, initially in a bosonic thermofield vacuum, and the output states, initially in vacuum states, evolve under a Liouville-von Neumann equation. 
Thiago Prudencio
quant-ph hep-th