Analytical evaluation of the coefficients of the Hu-Paz-Zhang master equation: Ohmic spectral density, zero temperature, and consistency check

TL;DR

This paper analytically evaluates the coefficients of the Hu-Paz-Zhang master equation for a quantum harmonic oscillator with Ohmic spectral density at zero temperature, examining its consistency, positivity, and parameter boundaries.

Contribution

It provides the first analytical evaluation of the coefficients of this non-Markovian master equation under specific spectral density and temperature conditions.

Findings

Confirmed the positivity of the stationary density operator.

Identified parameter boundaries for the model.

Analyzed the consistency of the solutions.

Abstract

We investigate the exact master equation of Hu, Paz, and Zhang for a quantum harmonic oscillator at zero temperature with a Lorentz-Drude type Ohmic spectral density. This master equation plays an important role in the study of quantum Brownian motion and in various applications. In this paper, we give an analytical evaluation of the coefficients of this non-Markovian master equation without Lindblad form, which allows us to investigate consistencies of the solutions, the positivity of the stationary density operator, and the boundaries of the model's parameters.