Stochastic Bloch-Redfield theory: Quantum jumps in a solid-state environment

We discuss mapping the Bloch-Redfield master equation to Lindblad form and then unraveling the resulting evolution into a stochastic Schrodinger 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 unraveling of the Bloch-Redfield equations becomes the kinetic Monte Carlo algorithm in the secular approximation when the system-bath-coupling operators are given by tunneling operators between system eigenstates. The stochastic unraveling is compared to the conventional Bloch-Redfield approach with the superconducting single-electron transistor (SSET) as an example.