Solution of the Master Equation for Quantum Brownian Motion given by the Schr\"{o}dinger Equation

TL;DR

This paper demonstrates how the master equation for quantum Brownian motion can be transformed into an autonomous one-dimensional Schrödinger equation using group invariant transformations, simplifying its solution.

Contribution

It introduces a method to reduce the quantum Brownian motion master equation to an equivalent Schrödinger equation via symmetry transformations, offering a new analytical approach.

Findings

Master equation can be transformed into a Schrödinger equation

Existence of a surface where the solution simplifies

Provides a new analytical tool for quantum Brownian motion

Abstract

We consider the master equation of quantum Brownian motion and with the application of the group invariant transformation we show that there exists a surface on which the solution of the master equation is given by an autonomous one-dimensional Schr\"{o}dinger Equation.