Microscopic foundation of a finite-temperature stochastic Schrödinger equation

We present a microscopic derivation of a stochastic Schrödinger equation for an oscillator valid at finite temperatures. Damping and noise arise from interaction with a heat bath. Vacuum and thermal noise drive the wavevector in rather different ways which we illuminate by treating the fate of an initial Schrödinger cat state. While the decoherence of the two macroscopically distinct components of such a state is thermally enhanced, the rise of a classically interpretable signal indicating `life' or `death' is not. Suitable averages over the noises could be obtained from a well known master equation and demand interpretation in terms of ensembles, but results contingent on single realizations of the noises may be related to single runs of experiments.