We have previously pointed out (1996, Phys. Rev. Lett. 77, 798) that in the calculation of a correlation function C(t) by means of the fluctuation dissipation theorem, much insight could be gained by writing the Fourier transform of C(t) as of the Fourier transform of the relaxation function multiplying the universal power spectrum of quantum noise at temperature T. Here, we show how this factorization leads to an immediate simplifying approach in the weak coupling limit near resonance. In particular, the time decay dependencies which appear are those associated with the Onsager classical regression theorem. Also, we throw further light on our previous assertion that there is never a quantum regression theorem. 1999 Academic Press Correlation functions are an integral component of the literature of statistical physics [1, 2] and they have applications in many different branches of physics. In particular, they arise in the work of Callen and Welton on the fluctuation dissipation theorem [3, 4] and the work of Kubo et al.
[1] on linear response theory. The relationship between correlation functions and relaxation (after-effect) functions has also proved to be very useful [1,5].
Another pillar of nonequilibrium statistical physics is the famous Onsager regression hypothesis [6], which he used to obtain his equally famous reciprocity law of kinetic coefficients. This hypothesis states that ``the average regression of fluctuations will obey the same laws as the corresponding macroscopic irreversible process' ' [6] and it should be emphasized that it is a statement of classical statistical physics. In fact, in the classical limit and for macroscopic variables corresponding to a dynamical variable of the system, the fluctuation dissipation theorem is a proof of the Onsager regression hypothesis [5].
Correlation functions are pervasive in Quantum Optics and one often needs to study the correlation of many operators at different times. In particular, they arise