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

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 it is subject to approximations, like the weak coupling limit. 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 weak coupling limit, the positivity of the stationary density operator, and the boundaries of the model's parameters.