Adjoint master equation for quantum Brownian motion

Quantum Brownian motion is a fundamental model for a proper understanding of open quantum systems in different contexts such as chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper we propose a different approach to describe this model. We provide an exact and analytic equation for the time evolution of the operators and we show that the corresponding equation for the states is equivalent to well-known results in the literature. The dynamics is expressed in terms of the spectral density, regardless of the strength of the coupling between the system and the bath. Our derivation allows to compute the time evolution of physically relevant quantities in a much easier way than previous formulations. An example is explicitly studied.