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arXiv · 1310.0559

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

Nicolas Vogt·Jan Jeske·Jared H. Cole
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Abstract

We discuss mapping the Bloch-Redfield master-equation to Lindblad form and then unravelling the resulting evolution into a stochastic Schrödinger 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.

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Nicolas Vogt, Jan Jeske, Jared H. Cole. 2013-12-06. Stochastic Bloch-Redfield theory: quantum jumps in a solid-state environment. https://doi.org/10.1103/physrevb.88.174514

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