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DY: Fachverband Dynamik und Statistische Physik

DY 35: Poster: Quantum Dynamics and Many-body Systems

DY 35.20: Poster

Wednesday, March 20, 2024, 15:00–18:00, Poster D

A margin of stability in the propagation of open quantum systems — •Malte Krug and Jürgen Stockburger — Institute for Complex Quantum Systems, Ulm University

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 a non-perturbative method, suitable also for strong coupling and sluggish environments with long-time correlations [1]. In spite of the wide range of successful applications of HEOM, there are certain instances where the necessary finite truncation of the hierarchy of auxiliary density operators leads to divergent solutions. We present results on the nature and causes of this type of critical error based on analytic results and numerical experiments [2]. Both the case of pure decoherence, where exact results are available for comparison, and divergences in certain parameter regions of the spin-boson model are investigated. 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.

[1] Xu, M., Yan, Y., Shi, Q., Ankerhold, J. and Stockburger, J.T. Taming quantum noise for efficient low temperature simulations of open quantum systems Phys. Rev. Lett. 129, 230601 (2022).
https://doi.org/10.1103/PhysRevLett.129.230601.

[2] Krug, M., Stockburger, J. On stability issues of the HEOM method. Eur. Phys. J. Spec. Top. (2023).
https://doi.org/10.1140/epjs/s11734-023-00972-9.

Keywords: open quantum system; hierarchical equations of motion; quantum dynamics; quantum thermodynamics