Random-matrix model for quantum Brownian motion

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.