Exploiting the path-integral radius of gyration in open quantum dynamics

• URL: http://arxiv.org/abs/2602.14647v1
• Date: Mon, 16 Feb 2026 11:10:24 GMT
• Title: Exploiting the path-integral radius of gyration in open quantum dynamics
• Authors: Andrew C. Hunt, Stuart C. Althorpe,
• Abstract summary: A major challenge in open quantum dynamics is the inclusion of Matsubara-decay terms in the memory kernel.<n>We show that the well-known Ishizaki--Tanimura correction is equivalent to separating smooth from Brownian' contributions.<n>We also develop a simple A4' adaptation of the AAA' algorithm in order to fit $mathcal R2()$ to a sum over poles.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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