Cauchy-Schwarz bound on the accuracy of truncated models in non-relativistic quantum electrodynamics
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913728683835392 |
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| author | Eyles, Daniel Stokes, Adam Nazir, Ahsan |
| author_facet | Eyles, Daniel Stokes, Adam Nazir, Ahsan |
| contents | We show that the Cauchy-Schwarz inequality provides a simple yet general bound that limits the accuracy of light-matter theories which retain only finite numbers of material energy levels. A corollary is that unitary rotations within a truncated space cannot transform between gauges, because the contrary assumption yields incorrect predictions. In particular, a widespread model obtained using such a rotation and treated as a Coulomb gauge model within a substantial body of literature, yields incorrect predictions under this assumption. The simplest system of a single dipole coupled to a single photonic mode in one spatial dimension is analysed in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07791 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cauchy-Schwarz bound on the accuracy of truncated models in non-relativistic quantum electrodynamics Eyles, Daniel Stokes, Adam Nazir, Ahsan Quantum Physics Mesoscale and Nanoscale Physics We show that the Cauchy-Schwarz inequality provides a simple yet general bound that limits the accuracy of light-matter theories which retain only finite numbers of material energy levels. A corollary is that unitary rotations within a truncated space cannot transform between gauges, because the contrary assumption yields incorrect predictions. In particular, a widespread model obtained using such a rotation and treated as a Coulomb gauge model within a substantial body of literature, yields incorrect predictions under this assumption. The simplest system of a single dipole coupled to a single photonic mode in one spatial dimension is analysed in detail. |
| title | Cauchy-Schwarz bound on the accuracy of truncated models in non-relativistic quantum electrodynamics |
| topic | Quantum Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2503.07791 |