Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Lampert, Lance Gadamsetty, Srikar Chaudhary, Shantanu Pei, Yiting Chen, Jiahao Crowder, Elyana Davidović, Dragomir |
| author_facet | Lampert, Lance Gadamsetty, Srikar Chaudhary, Shantanu Pei, Yiting Chen, Jiahao Crowder, Elyana Davidović, Dragomir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity Lampert, Lance Gadamsetty, Srikar Chaudhary, Shantanu Pei, Yiting Chen, Jiahao Crowder, Elyana Davidović, Dragomir Quantum Physics 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. |
| title | Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.11088 |