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arXiv · 1602.03971

Time-local Heisenberg-Langevin equations and the driven qubit

S. J. Whalen·H. J. Carmichael
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Abstract

The time-local master equation for a driven boson system interacting with a boson environment is derived by way of a time-local Heisenberg--Langevin equation. Extension to the driven qubit fails---except for weak excitation---due to the lost linearity of the system-environment interaction. We show that a reported time-local master equation for the driven qubit is incorrect. As a corollary to our demonstration, we also uncover odd asymptotic behavior in the "repackaged" time-local dynamics of a system driven to a far-from-equilibrium steady state: the density operator becomes steady while time-dependent coefficients oscillate (with periodic singularities) forever.

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S. J. Whalen, H. J. Carmichael. 2016-02-12. Time-local Heisenberg-Langevin equations and the driven qubit. https://doi.org/10.1103/physreva.93.063820

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