On truncations of hierarchical equations of motion for finite-dimensional systems
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908991104221184 |
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| author | Vadimov, Vasilii |
| author_facet | Vadimov, Vasilii |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22568 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On truncations of hierarchical equations of motion for finite-dimensional systems Vadimov, Vasilii Quantum Physics Mathematical Physics 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. |
| title | On truncations of hierarchical equations of motion for finite-dimensional systems |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2604.22568 |