Cold, Dilute, Trapped Bosons as an Open Quantum System

We present a master equation governing the reduced density operator for a single trapped mode of a cold, dilute, weakly interacting Bose gas, and we obtain an operator fluctuation-dissipation relation in which the Ginzburg-Landau effective potential plays a physically transparent role. We also identify a decoherence effect that tends to preserve symmetry, even when the effective potential has a ``Mexican hat'' form.