Adjoint master equation for Quantum Brownian Motion

TL;DR

This paper introduces an exact, analytic operator equation for quantum Brownian motion that simplifies the calculation of system dynamics regardless of coupling strength, enhancing understanding of open quantum systems.

Contribution

It presents a novel, exact operator equation for quantum Brownian motion dynamics, applicable for any coupling strength, simplifying calculations of physical quantities.

Findings

Provides an exact and analytic operator evolution equation.

Demonstrates equivalence with known state evolution results.

Simplifies computation of physical quantities in quantum Brownian motion.

Abstract

Quantum brownian motion is a fundamental model for a proper understanding of open quantum systems in different contexts such as chemistry, condensed matter physics, bio-physics and opto- mechamics. In this paper we propose a novel approach to describe this model. We provide an exact and analytic equation for the time evolution of the operators, and we show that the corresponding equation for the states is equivalent to well-known results in literature. The dynamics is expressed in terms of the spectral density, regardless the strength of the coupling between the system and the bath. Our allows to compute the time evolution of physically relevant quantities in a much easier way than previous formulations allow to. An example is explicitly studied.