Quantum statistical effects of the motion of an oscillator interacting with a radiation field

The motion of a quantum oscillator interacting with a quantized radiation field is studied. The exact solution shows that the motion of the oscillator is described by a Langevin-type equation in which the friction and the effective frequency depend on time. The physical conditions under which these properties become constant are studied. The stochastic force becomes a gaussian process and in the limit of long times and weak coupling, has an autocorrelation function with the usual delta behavior.