  We discuss mapping the Bloch-Redfield master-equation to Lindblad form and
then unravelling the resulting evolution into a stochastic Schr\"odinger
equation according to the quantum-jump method. We give two approximations under
which this mapping is valid. This approach enables us to study
solid-state-systems of much larger sizes than is possible with the standard
Bloch-Redfield master-equation, while still providing a systematic method for
obtaining the jump operators and corresponding rates. We also show how the
stochastic unravelling of the Bloch-Redfield equations becomes the kinetic
Monte Carlo (KMC) algorithm in the secular approximation when the
system-bath-coupling operators are given by tunnelling-operators between
system-eigenstates. The stochastic unravelling is compared to the conventional
Bloch-Redfield approach with the superconducting single electron transistor
(SSET) as an example.
