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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2603.25639 |
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| _version_ | 1866912983919099904 |
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| author | Bondar, Denys I. Steuernagel, Ole |
| author_facet | Bondar, Denys I. Steuernagel, Ole |
| contents | In this methods paper, we show how to tridia\-go\-nalize two families of bosonic multimode systems: optomechanical and Bose-Hubbard hamiltonians. Using tools from number theory, we devise a rendering of these systems in the form of exact $D \times D$ tridiagonal symmetric matrices with real-valued entries. Such matrices can subsequently be exactly diagonalized using specialized sparse-matrix algorithms that need on the order of $D \ln(D)$ steps. This makes it possible to describe systems with much larger numbers of basis states than available to date. It also allows for efficient diagonal representation of large, accurate, symplectic split-operator propagators for which we moreover show that the required basis changes can be implemented by simple re-indexing, at marginal computational cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25639 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symplectic Split-Operator Propagators from Tridiagonalized Multi-Mode Bosonic Hilbert Spaces for Bose-Hubbard Hamiltonians Bondar, Denys I. Steuernagel, Ole Quantum Physics In this methods paper, we show how to tridia\-go\-nalize two families of bosonic multimode systems: optomechanical and Bose-Hubbard hamiltonians. Using tools from number theory, we devise a rendering of these systems in the form of exact $D \times D$ tridiagonal symmetric matrices with real-valued entries. Such matrices can subsequently be exactly diagonalized using specialized sparse-matrix algorithms that need on the order of $D \ln(D)$ steps. This makes it possible to describe systems with much larger numbers of basis states than available to date. It also allows for efficient diagonal representation of large, accurate, symplectic split-operator propagators for which we moreover show that the required basis changes can be implemented by simple re-indexing, at marginal computational cost. |
| title | Symplectic Split-Operator Propagators from Tridiagonalized Multi-Mode Bosonic Hilbert Spaces for Bose-Hubbard Hamiltonians |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.25639 |