Statistical correlations in the oscillator model of quantum dissipative systems

Summary

We study the problem of the initial conditions for the oscillator model of quantum dissipative systems. It is argued that, even in the classical case, the hypothesis that the environment is in thermal equilibrium implies a statistical correlation between the environment and the central system. Analogously to the classical model, we obtain a simple form of initial conditions for the quantum problem that takes into account such a correlation. As a check on the new form of correlated initial conditions, we study the forced Brownian particle with arbitrary coloured noise. On the one hand, starting from the correlated initial conditions, we show that the average position of a wave packet is equal to that of the corresponding classical Brownian particle. On the other hand, starting from the initial conditions based on the factorization hypothesis, that implies absence of correlation, nonphysical results are obtained.