Strong damping and low-temperature anomalies for the harmonic oscillator

We consider Ullersma’s model of a damped harmonic oscillator interacting with a heat bath. We show that for large damping the oscillator does not undergo Brownian motion at any temperature. For high temperatures non-Markovian effects show up in initial slips only. For low temperatures we find, as further anomalies, power-law decay of time-dependent expectation values as well as a strong squeezing of the displacement and momentum uncertainties; again these anomalies are most strongly pronounced for strong damping.