On truncations of hierarchical equations of motion for finite-dimensional systems

Abstract:We study truncations of hierarchical equations of motion (HEOM) for finite-dimensional open quantum systems. We prove that for finite-dimensional approximations constructed with a Schur-complement type of terminator, the spectrum converges to that of the full HEOM as the truncation depth increases. We also prove that this approximation is free of spectral pollution: sufficiently deep truncations do not produce spurious unstable modes, provided the exact HEOM is stable. We illustrate the results for the spin-boson model.

arXiv:2604.22568 [quant-ph]

(or arXiv:2604.22568v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.22568 Focus to learn more arXiv-issued DOI via DataCite

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