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arXiv · 2406.11088

Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity

Lance Lampert·Srikar Gadamsetty·Shantanu Chaudhary·Yiting Pei·Jiahao Chen·Elyana Crowder·Dragomir Davidović
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Abstract

Perturbative master equations are essential for modeling open quantum systems but often exhibit late-time divergences when environmental correlations decay algebraically. In this work, we analyze the time-convolutionless (TCL) master equation, expanded to order 2n and demonstrate that, while van Kampens cumulants suppress early-time secular growth, they ultimately diverge at long times. To overcome this, we introduce a resummation technique based on the Hadamard trick, which incorporates time integrals directly into the bath spectral density via element-wise multiplication. This approach establishes a maximum expansion order, nmax, and defines a precision limit of the asymptotic states. The resummed master equation features renormalized Bohr frequencies that capture decoherence and spectral overlap effects. In the unbiased spin-boson model, this results in secular inflation of the generator at a temperature-independent rate equal to the decoherence rate and a finite validity time. For exponentially decaying correlations, the method recovers a proper Markovian limit below a critical coupling threshold.

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Lance Lampert, Srikar Gadamsetty, Shantanu Chaudhary, Yiting Pei, Jiahao Chen, Elyana Crowder, Dragomir Davidović. 2024-06-16. Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity. https://doi.org/10.1103/physreva.111.042214

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