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 behaviour occurs for strong coupling. The dynamical evolution of the quantum purity for a single and a double wave packet is also investigated.
Highlights
The dissipative harmonic oscillator has for long attracted considerable interest as a prototype of open quantum system
We argue that a harmonic oscillator coupled through position and momentum to two independent baths is a suitable representation of large spin impurity in a ferromagnetic system
It describes a harmonic oscillator with momentum p and position q, each variable being coupled to a different oscillator bath
Summary
The dissipative harmonic oscillator has for long attracted considerable interest as a prototype of open quantum system. There it was argued that a complex dissipative environment can be modelled by a bath of harmonic oscillators, with the couplings parameters chosen to yield a Langevin equation for the q variable in the semiclassical limit. It was shown later [20] We argue that a harmonic oscillator coupled through position and momentum to two independent baths is a suitable representation of large spin impurity in a ferromagnetic system. We find that the most prominent feature of the double–bath model, namely, the existence of underdamped oscillations for arbitrarily strong coupling, disappears in the case of single–bath dissipation
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