Exploiting the path-integral radius of gyration in open quantum dynamics
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
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2026
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| _version_ | 1866914331920171008 |
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| author | Hunt, Andrew C. Althorpe, Stuart C. |
| author_facet | Hunt, Andrew C. Althorpe, Stuart C. |
| contents | A major challenge in open quantum dynamics is the inclusion of Matsubara-decay terms in the memory kernel, which arise from the quantum-Boltzmann delocalisation of the bath modes. This delocalisation can be quantified by the radius of gyration squared ${\mathcal R}^2(ω)$ of the imaginary-time Feynman paths of the bath modes as a function of the frequency $ω$. In a Hierarchical Equations of Motion (HEOM) calculation with a Debye--Drude spectral density, ${\mathcal R}^2(ω)$ is the only quantity that is treated approximately (assuming convergence with respect to hierarchy depth). Here, we show that the well-known Ishizaki--Tanimura correction is equivalent to separating smooth from `Brownian' contributions to ${\mathcal R}^2(ω)$, and that modifying the correction leads to a more efficient HEOM in the case of fast baths. We also develop a simple `A4' adaptation of the `AAA' (Adaptive Antoulas--Anderson) algorithm in order to fit ${\mathcal R}^2(ω)$ to a sum over poles, which results in an extremely efficient implementation of the standard HEOM method at low temperatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14647 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exploiting the path-integral radius of gyration in open quantum dynamics Hunt, Andrew C. Althorpe, Stuart C. Quantum Physics Chemical Physics A major challenge in open quantum dynamics is the inclusion of Matsubara-decay terms in the memory kernel, which arise from the quantum-Boltzmann delocalisation of the bath modes. This delocalisation can be quantified by the radius of gyration squared ${\mathcal R}^2(ω)$ of the imaginary-time Feynman paths of the bath modes as a function of the frequency $ω$. In a Hierarchical Equations of Motion (HEOM) calculation with a Debye--Drude spectral density, ${\mathcal R}^2(ω)$ is the only quantity that is treated approximately (assuming convergence with respect to hierarchy depth). Here, we show that the well-known Ishizaki--Tanimura correction is equivalent to separating smooth from `Brownian' contributions to ${\mathcal R}^2(ω)$, and that modifying the correction leads to a more efficient HEOM in the case of fast baths. We also develop a simple `A4' adaptation of the `AAA' (Adaptive Antoulas--Anderson) algorithm in order to fit ${\mathcal R}^2(ω)$ to a sum over poles, which results in an extremely efficient implementation of the standard HEOM method at low temperatures. |
| title | Exploiting the path-integral radius of gyration in open quantum dynamics |
| topic | Quantum Physics Chemical Physics |
| url | https://arxiv.org/abs/2602.14647 |