  In this paper we demonstrate how to generate the strong-coupling master
equations for open quantum systems of continuous variables. These are the
dissipative master equations of quantum Brownian particles for which the
environmental noise is stronger than other system forces. Our strong-coupling
master equations are very different from other so-called "strong-coupling"
master equations (e.g. the quantum Smoluchowski equation) which are perturbing
off a limit in which the system energy is taken to be perturbative and thus the
dynamics is principally Markovian. Such approximations also require the system
mass to be asymptotically large (even as compared to the ratio of noise and
induced system frequencies) and thus they do not fully categorize the regime of
what one might consider to be strong coupling. Our master equations are highly
non-Markovian and radically different for different system potentials,
admitting no apparent generic form. This result is quite exciting as it brings
forth a new regime for theoretical exploration: the regime of strong noise and
dissipation yet non-Markovian, such as strong coupling to a low-temperature
environment with large 1/f fluctuations.
