Dissipative quantum oscillator with two competing heat baths

Abstract

We study the dissipative dynamics of a harmonic oscillator which couples linearly through its position and its momentum to two independent heat baths at the same temperature. We argue that this model describes a large spin in a ferromagnet. We find that some effects of the two heat baths partially cancel each other. This leads to unexpected features such as underdamped oscillations and long relaxation times in the strong coupling regime. Such a partial frustration of dissipation can be ascribed to the canonically conjugate character of position and momentum. We compare this model to the scenario where a single heat bath couples linearly to both the position and the momentum of the central oscillator. In that case less surprising behavior occurs for strong coupling. The dynamical evolution of the quantum purity for a single and a double wave packet is also investigated.