U(1) and SU(2) quantum dissipative systems: The Caldeira-Leggett vs. the Amegaokar-Eckern-Sch\"on approaches

TL;DR

This paper compares two main theoretical frameworks for modeling quantum dissipative systems, specifically analyzing their differences and implications for a zero-dimensional spin in a dissipative quantum dot environment.

Contribution

It clarifies the distinctions between the Caldeira-Leggett and Ambegaokar-Eckern-Sch"on approaches and explores their effects on SU(2) symmetric quantum systems.

Findings

Differences between the two frameworks are elucidated.

Implications for dissipative quantum dots near the Stoner instability are discussed.

Theoretical insights into SU(2) quantum dissipative systems are provided.

Abstract

There are two paradigmatic frameworks for treating quantum systems coupled to a dissipative environment: the Caldeira-Leggett and the Ambegaokar-Eckern-Sch\"on approaches. Here we recall the differences between them, and explain the consequences when each is applied to a zero dimensional spin (possessing an SU(2) symmetry) in a dissipative environment (a dissipative quantum dot near or beyond the Stoner instability point).