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

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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• Coupled charge and energy transfer dynamics in light harvesting complexes from a hybrid hierarchical equations of motion approach
• Managing Temperature in Open Quantum Systems Strongly Coupled with Structured Environments
• Charge transport limited by nonlocal electron-phonon interaction. I. Hierarchical equations of motion approach
• General Framework for Quantifying Dissipation Pathways in Open Quantum Systems. II. Numerical Validation and the Role of Non-Markovianity
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime
• About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach
• Numerically "exact" charge transport dynamics in a dissipative electron-phonon model rationalizing the success of the transient localization scenario
• General framework for quantifying dissipation pathways in open quantum systems. III. Off-diagonal system-bath couplings
• Applicability of the cumulant expansion method for the calculation of transport properties in electron-phonon systems