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

Nicolas Vogt, Jan Jeske, and Jared H. Cole
Phys. Rev. B 88, 174514 – Published 19 November 2013

Abstract

We discuss mapping the Bloch-Redfield master equation to Lindblad form and then unraveling 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 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.

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  • Received 3 October 2013

DOI:https://doi.org/10.1103/PhysRevB.88.174514

©2013 American Physical Society

Authors & Affiliations

Nicolas Vogt1,2, Jan Jeske3, and Jared H. Cole3

  • 1Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany
  • 2DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany
  • 3Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne, Australia

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Issue

Vol. 88, Iss. 17 — 1 November 2013

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