A new non-perturbative approach to Quantum Brownian Motion

TL;DR

This paper introduces a non-perturbative derivation of the quantum Brownian motion equation from the Caldeira-Leggett model, providing explicit temperature-dependent diffusion constants and analyzing positivity conditions at various temperatures.

Contribution

It presents a new non-perturbative approach to derive the quantum Brownian motion equation directly from the Caldeira-Leggett model, clarifying diffusion behavior across temperature regimes.

Findings

Explicit temperature dependence of diffusion constants derived.

Classical Langevin equation recovered at high temperatures.

Positivity of the density matrix violated below a critical temperature.

Abstract

Starting from the Caldeira-Leggett (CL) model, we derive the equation describing the Quantum Brownian motion, which has been originally proposed by Dekker purely from phenomenological basis containing extra anomalous diffusion terms. Explicit analytical expressions for the temperature dependence of the diffusion constants are derived. At high temperatures, additional momentum diffusion terms are suppressed and classical Langivin equation can be recovered and at the same time positivity of the density matrix(DM) is satisfied. At low temperatures, the diffusion constants have a finite positive value, however, below a certain critical temperature, the Master Equation(ME) does not satisfy the positivity condition as proposed by Dekker.