Local topology for periodic Hamiltonians and fuzzy tori
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912430527873024 |
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| author | Doll, Nora Loring, Terry Schulz-Baldes, Hermann |
| author_facet | Doll, Nora Loring, Terry Schulz-Baldes, Hermann |
| contents | A variety of local index formulas is constructed for quantum Hamiltonians with periodic boundary conditions. All dimensions of physical space as well as many symmetry constraints are covered, notably one-dimensional systems in Class DIII as well as two- and three-dimensional systems in Class AII. The constructions are based on several periodic variations of the spectral localizer and are rooted in the existence of underlying fuzzy tori. For these latter, a general invariant theory is developed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local topology for periodic Hamiltonians and fuzzy tori Doll, Nora Loring, Terry Schulz-Baldes, Hermann Mathematical Physics Disordered Systems and Neural Networks A variety of local index formulas is constructed for quantum Hamiltonians with periodic boundary conditions. All dimensions of physical space as well as many symmetry constraints are covered, notably one-dimensional systems in Class DIII as well as two- and three-dimensional systems in Class AII. The constructions are based on several periodic variations of the spectral localizer and are rooted in the existence of underlying fuzzy tori. For these latter, a general invariant theory is developed. |
| title | Local topology for periodic Hamiltonians and fuzzy tori |
| topic | Mathematical Physics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2403.18931 |