Sluggish decay of preparation effects in low temperature quantum systems

Abstract

We have discussed the time evolution of squeezed states coupled to an environment. By way of example we showed that the influence of the initial preparation may decay on a time scale much longer than the time scale for the classical relaxation to equilibrium. We have proposed two preparations (2 and 4) with the same reduced density matrix at t=0 where the initial correlations between system and bath influence the average relaxation for extremely long times at low temperatures. In another example (1 and 3) the correlation effects do not show up in the average relaxation of 〈p〉 and 〈q〉 but they are apparent in the time evolution of the second moments. These effects cannot be obtained within a weak coupling theory and become more pronounced as temperature is decreased. The commonly used approximation of factorizing initial states is then not necessarily well justified. It is expected that this behavior is of general relevance for dissipative quantum systems and not restricted to the special case considered here.

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