Asymptotics of means in a non-equilibrium model of the Dicke type

The representation of the density matrix f o r the nonequilibrium system in terms of functional integrals is used for obtaining and the rigorous proof the asymptotic formulae for the averages of the radiation field interacting with a system of two-level atoms at $N\to\infty$ ($N$ is a number of atoms). The estimation method for functional integrals developed earlier for the equilibrium model system is used in the rigorous proof of the asymptotic formulae.