Drift, drag and Brownian motion in the Davies-Unruh bath

An interesting feature of the Davies-Unruh effect is that a uniformly accelerated observer sees an isotropic thermal spectrum of particles even though there is a preferred direction in this context, determined by the direction of the acceleration g. We investigate the thermal fluctuations in the Unruh bath by studying the Brownian motion of particles in the bath, especially as regards to isotropy. We find that the thermal fluctuations are anisotropic and induce different frictional drag forces on the Brownian particle depending on whether it has a drift velocity along the direction of acceleration g or in a direction transverse to it. Using the fluctuation-dissipation theorem, we argue that this anisotropy arises due to quantum correlations in the fluctuations at large correlation time scales.