Minimal coupling in oscillator models of quantum dissipation

TL;DR

This paper explores different models of quantum dissipation in harmonic oscillators, focusing on how coupling to baths via position or momentum affects their equivalence and physical relevance.

Contribution

It introduces and analyzes models where the oscillator couples to baths via both position and momentum, highlighting the lack of a unitary transformation between these representations.

Findings

Position and momentum couplings are related by a unitary transformation in single-bath models.

Coupling to separate baths via position and momentum cannot be transformed into each other.

The models have distinct physical implications and relevance.

Abstract

The dissipative harmonic oscillator has two representations. In the first representation the central oscillator couples with its position to an oscillator bath. In the second one it couples with its momentum to the bath. Both representations are related by a unitary transformation. If the central oscillator couples with its position and momentum to two independent baths, no such unitary transformation exists. We discuss two possible models of this type and their physical relevance.