The Extended Stochastic Liouville Equation

We present an exact approach to the evolution of density matrices for open quantum systems coupled to a general harmonic environment. This generalises and extends previous work based on Caldeira-Leggett models and a factorised initial density matrix. In particular, this method allows more general forms of environment-system couplings and initial conditions. The result is an exact stochastic description for the evolution of an arbitrary open system from a broad class of initial conditions, which we term the Extended Stochastic Liouville Equation (ELSE). This technique allows us to consider driving open systems from a coupled equilibrium with the environment, even in the strong-coupling regime. This is demonstrated analysing a driven spin-Boson model using the ESLE.