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

Vasilii Vadimov

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arXiv · 2604.22568

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

Vasilii Vadimov

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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.

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Vasilii Vadimov. 2026-04-24. On truncations of hierarchical equations of motion for finite-dimensional systems. https://arxiv.org/abs/2604.22568

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