Fock space: A bridge between Fredholm index and the quantum Hall effect
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909227520360448 |
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| author | Thiang, Guo Chuan Xia, Jingbo |
| author_facet | Thiang, Guo Chuan Xia, Jingbo |
| contents | We compute the quantized Hall conductance at various Landau levels by using the classic trace. The computations reduce to the single elementary one for the lowest Landau level. By using the theories of Helton-Howe-Carey-Pincus, and Toeplitz operators on the classic Fock space and higher Fock spaces, the Hall conductance is naturally identified with a Fredholm index. This brings new mathematical insights to the extraordinary precision of quantization observed in quantum Hall measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fock space: A bridge between Fredholm index and the quantum Hall effect Thiang, Guo Chuan Xia, Jingbo Mathematical Physics Mesoscale and Nanoscale Physics Functional Analysis Quantum Algebra We compute the quantized Hall conductance at various Landau levels by using the classic trace. The computations reduce to the single elementary one for the lowest Landau level. By using the theories of Helton-Howe-Carey-Pincus, and Toeplitz operators on the classic Fock space and higher Fock spaces, the Hall conductance is naturally identified with a Fredholm index. This brings new mathematical insights to the extraordinary precision of quantization observed in quantum Hall measurements. |
| title | Fock space: A bridge between Fredholm index and the quantum Hall effect |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Functional Analysis Quantum Algebra |
| url | https://arxiv.org/abs/2401.07449 |