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, bio-physics and opto- mechamics. In this paper we propose a novel 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 literature. The dynamics is expressed in terms of the spectral density, regardless the strength of the coupling between the system and the bath. Our allows to compute the time evolution of physically relevant quantities in a much easier way than previous formulations allow to. An example is explicitly studied.