Generalised regression theorem and correlation functions of fluctuation operators in quantum optics
L. Knöll · Journal of Physics A Mathematical and General · 1985
The author considers a dynamic system interacting with a special dissipative system composed of many harmonic oscillators. Using the Feynman disentangling theorem and a bath approximation he derives differential equations for correlation functions of dynamic operators (CFD) concerning the maximum time argument t which in general occurs in more than one operator. They must be solved with appropriate initial conditions at time t', the second in height time argument in the CFD. This procedure allows the successive calculation of CFD with an arbitrary time arrangement (e.g. CFD of three operators, where the central one carries the smallest time argument). The exact equations of motion for dynamic operators may also be written as Langevin equations. The author defines the corresponding fluctuation operators and derives compact expressions for their correlation functions (CFF). In general the fluctuation operators show no Gaussian behaviour. CFF of second order are delta -correlated and CFF of third order are only delta -correlated with respect to the two highest time arguments.