A simple improved low temperature correction for the hierarchical equations of motion

• URL: http://arxiv.org/abs/2205.09270v2
• Date: Wed, 29 Jun 2022 16:10:46 GMT
• Title: A simple improved low temperature correction for the hierarchical equations of motion
• Authors: Thomas P Fay
• Abstract summary: We propose a new low temperature correction scheme for the termination of the hierarchy based on Zwanzig projection. The utility of the new correction scheme is demonstrated on a range of model systems, including the Fenna-Metthews-Olson complex.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The study of open system quantum dynamics has been transformed by the hierarchical equations of motion (HEOM) method, which gives the exact dynamics for a system coupled to a harmonic bath at arbitrary temperature and system-bath coupling strength. However in its standard form the method is only consistent with the weak-coupling quantum master equation at all temperatures when many auxiliary density operators are included in the hierarchy, even when low temperature corrections are included. Here we propose a new low temperature correction scheme for the termination of the hierarchy based on Zwanzig projection which alleviates this problem, and restores consistency with the weak-coupling master equation with a minimal hierarchy. The utility of the new correction scheme is demonstrated on a range of model systems, including the Fenna-Metthews-Olson complex. The new closure is found to improve convergence of the HEOM even beyond the weak-coupling limit and is very straightforward to implement in existing HEOM codes.

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