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We study decoherence, diffusion, friction, and how they thermalize a planarrotor in the presence of an external potential. Representing the quantum masterequation in terms of auxiliary Wigner functions in periodic phase space notonly illustrates the thermalization process in a concise way, but also allowsfor an efficient numerical evaluation of the open quantum dynamics and itsapproximate analytical description. In particular, we analytically andnumerically verify the existence of a steady state that, in thehigh-temperature regime, closely approximates a Gibbs state. We also derive theproper classical limit of the planar rotor time evolution and present exemplarynumerical studies to verify our results.

Thermalization of the Quantum Planar Rotor with external potential