Dresden 2026 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 53: Nonequilibrium Quantum Systems II (joint session TT/DY)

TT 53.4: Talk

Wednesday, March 11, 2026, 15:45–16:00, HSZ/0105

Improving the stability of the hierarchical equations of motion approach for generic bosonic spectral densities — •Salvatore Gatto, Samuel Rudge, and Michael Thoss — University of Freiburg

The hierarchical equations of motion (HEOM) constitute a numerically exact method for investigating the dynamics of open quantum systems across a wide range of environmental conditions [1]. In this contribution, we investigate the stability of HEOM for generic bosonic spectral densities and identify temperature- and coupling-dependent instabilities in the time evolution. We show that, upon increasing the system-bath coupling strength, the conventional HEOM formulation may become unstable, and that simply extending the hierarchy depth does not cure these long-time divergences [2]. Starting from the HEOM structure, we derive a multidimensional phase-space differential equation that generalizes the Quantum Fokker-Planck equation to arbitrary temperature [3]. We further demonstrate that expanding this new equation in an alternative basis removes the numerical instabilities inherent to the standard HEOM representation.
[1] J. Bätge, Y. Ke, C. Kaspar, M. Thoss, PRB 103, 235413 (2021)
[2] I. S. Dunn, R. Tempelaar, D. R. Reichman, J. Chem. Phys. 150, 184109 (2019)
[3] T. Li, Y. Yan, and Q. Shi, J. Chem. Phys. 156, 064107 (2022)

Keywords: Nonperturbative methods; Path integrals; Open quantum systems