Universality of quantum Brownian motion

TL;DR

This paper demonstrates that Markovian master equations for quantum Brownian motion are universal, independent of specific model assumptions, by deriving them using a random band-matrix approach and confirming their agreement with established models.

Contribution

The authors introduce a random band-matrix model to derive universal Markovian master equations for quantum systems coupled to a heat bath, confirming their consistency with prior models.

Findings

Master equations agree with Caldeira-Legget and Agarwal models

Results hold in large-band limit and with/without rotating-wave approximation

Proves universality of quantum Brownian motion master equations

Abstract

Are Markovian master equations for quantum Brownian motion independent of model assumptions used in the derivation and, thus, universal? With the aim of answering this question, we use a random band-matrix model for the system-bath interaction to derive Markovian master equations for the time evolution of one-dimensional quantum systems weakly coupled to a heat bath. We study in detail two simple systems, the harmonic oscillator and the two-level system. Our results are in complete agreement with those of earlier models, like the Caldeira-Legget model and, in the large-band limit, with the Agarwal equations (both with and without rotating-wave approximation). This proves the universality of these master equations.