  Are Markovian master equations for quantum Brownian motion independent of
model assumptions used in the derivation and, thus, universal? With the aim of
answering this question, we use a random band-matrix model for the system-bath
interaction to derive Markovian master equations for the time evolution of
one-dimensional quantum systems weakly coupled to a heat bath. We study in
detail two simple systems, the harmonic oscillator and the two-level system.
Our results are in complete agreement with those of earlier models, like the
Caldeira-Legget model and, in the large-band limit, with the Agarwal equations
(both with and without rotating-wave approximation). This proves the
universality of these master equations.
