Abstract
A systematic method is proposed for calculating the density matrix of subsystems interacting with their environment under conditions of thermodynamic equilibrium. The density matrix of photons resonantly interacting with a surrounding gas is calculated. It is shown that use of the Gibbs distribution allows one to completely eliminate inelastic processes from the calculations. A correct account of photon-photon correlators indicates the presence of new cooperative effects. A new branch of the polariton spectrum is predicted, which is due to the presence of excited atoms in the medium. With the help of the density matrix the mean filling numbers of the photon modes are calculated. In terms of wavelengths, we have obtained a generalization of the Planck formula which accounts for photon cooperative phenomena. The manifestation of these effects in kinetic processes is discussed.
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