  We present an application of the Extended Stochastic Liouville Equation
(ESLE) Phys. Rev. B 95, 125124, which gives an exact solution for the reduced
density matrix of an open system surrounded by a harmonic heat bath. This
method considers the extended system (the open system and the bath) being
thermally equilibrated prior to the action of a time dependent perturbation, as
opposed to the usual assumption that system and bath are initially partitioned.
This is an exact technique capable of accounting for arbitrary parameter
regimes of the model. Here we present our first numerical implementation of the
method in the simplest case of a Caldeira-Leggett representation of the bath
Hamiltonian, and apply it to a spin-Boson system driven from coupled
equilibrium. We observe significant behaviours in both the transient dynamics
and asymptotic states of the reduced density matrix not present in the usual
approximation.
