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Thermal radiation fields in time-dependent linear media at finite temperature

The properties of thermal radiation fields in linear media which have time-dependent parameters are investigated on the basis of the invariant operator method. For quantum mechanical description of the electromagnetic waves whose amplitude and/or frequency vary with time, we introduce a quadratic invariant operator that is constructed according to its exact definition. The density operator of the system, being considered signal plus noise, is obtained via maximization of the entropy. The expectation values of the energy operator, the Hamiltonian, and the invariant operator are obtained in the thermal state and their thermal behaviours are illustrated in detail. It is shown that the fluctuations of the electric and the magnetic fields do not depend on signal plus noise and dissipate with time due to the conductivity in media. Our theory of wave propagation in time-varying media is applied to describe the biophoton signal in order to promote the understanding of our developments.