Quasiclassical frustration

We study the dissipative properties of a harmonic oscillator subject to two independent heat baths, one of which couples to its position and the other one to its momentum. This model describes a large spin impurity in a ferromagnet. We find that some effects of the two heat baths partially cancel each other. Most notably, oscillations may remain underdamped for arbitrarily strong coupling. This effect is a direct consequence of the mutually conjugate character of position and momentum. For a single dissipative bath coupled linearly to both position and momentum, no underdamped regime is possible for strong coupling. The dynamics of purity loss for one and two wave packets is also investigated.