On stability issues of the HEOM method
- URL: http://arxiv.org/abs/2408.05520v1
- Date: Sat, 10 Aug 2024 11:13:18 GMT
- Title: On stability issues of the HEOM method
- Authors: Malte Krug, Jürgen Stockburger,
- Abstract summary: We show that the necessary truncation of the hierarchy of auxiliary density operators seems to introduce errors which are not fully controllable.
We find that truncating the hierarchy to any finite size can be problematic for strong coupling to a dissipative reservoir.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The Hierarchical Equations of Motion (HEOM) method has become one of the cornerstones in the simulation of open quantum systems and their dynamics. It is commonly referred to as a non-perturbative method. Yet, there are certain instances, where the necessary truncation of the hierarchy of auxiliary density operators seems to introduce errors which are not fully controllable. We investigate the nature and causes of this type of critical error both in the case of pure decoherence, where exact results are available for comparison, and in the spin-boson system, a full system-reservoir model. We find that truncating the hierarchy to any finite size can be problematic for strong coupling to a dissipative reservoir, in particular when combined with an appreciable reservoir memory time.
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