Short-time behavior of the correlation functions for the quantum Langevin equation

We analyze the quantum Langevin equation obtained for the Ford-Kac-Mazur and related models. We study an explicit expression for the correlation function of the noise, obtained by making use of the normal-ordered product of operators. Such an expression is divergence-free, does not require any frequency cutoff, and yields the classical (Markoffian) case in the limit of vanishing h. We also bring to light and discuss two different regimes for the momentum autocorrelation. The high-temperature and weak-coupling limits are considered, and the latter is shown to be related to van Hove's ''lambda(2)T'' Limit.