Quasiclassical frustration

TL;DR

This paper investigates a harmonic oscillator coupled to two heat baths affecting position and momentum, revealing that their effects can partially cancel, allowing oscillations to remain underdamped even at strong coupling, due to the conjugate nature of position and momentum.

Contribution

It introduces a model with two independent heat baths affecting position and momentum, showing unique damping behavior not seen with single baths, highlighting the conjugate relationship's impact.

Findings

Oscillations can stay underdamped at strong coupling due to bath effects cancellation.

Mutually conjugate position and momentum baths lead to unique dissipative dynamics.

Single bath coupling cannot produce underdamped oscillations at strong coupling.

Abstract

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.