We use a random band-matrix model for the system-bath interaction to derive a Markovian master equation for the time evolution of one-dimensional quantum systems weakly coupled to a heat bath. We study in detail the damped harmonic oscillator and discuss the fluctuation-dissipation relation. In the large-bandwidth, high-temperature limit, our master equation coincides with the equations derived by Agarwal and Caldeira-Leggett. This shows that the Markovian master equations for quantum Brownian motion are independent of model assumptions used in their derivation and, thus, universal.
Lutz, E. (2001). Random-matrix model for quantum Brownian motion. Physica E: Low-Dimensional Systems and Nanostructures, 9(3), 369–373. https://doi.org/10.1016/S1386-9477(00)00230-7