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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2209.07468 |
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| _version_ | 1866910347708858368 |
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| author | LeClair, André |
| author_facet | LeClair, André |
| contents | We propose a formula constructed out of elementary functions that captures many of the detailed features of the transverse resistivity $ρ_{xy}$ for the integer quantum Hall effect. It is merely a phenomenological formula in the sense that it is not based on any transport calculation for a specific class of physical models involving electrons in a disordered landscape, thus, whether a physical model exists which realizes this resistivity remains an open question. Nevertheless, since the formula involves the Riemann zeta function and its non-trivial zeros play a central role, it is amusing to consider the implications of the Riemann Hypothesis in light of it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_07468 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Phenomenological formula for Quantum Hall resistivity based on the Riemann zeta function LeClair, André Mesoscale and Nanoscale Physics We propose a formula constructed out of elementary functions that captures many of the detailed features of the transverse resistivity $ρ_{xy}$ for the integer quantum Hall effect. It is merely a phenomenological formula in the sense that it is not based on any transport calculation for a specific class of physical models involving electrons in a disordered landscape, thus, whether a physical model exists which realizes this resistivity remains an open question. Nevertheless, since the formula involves the Riemann zeta function and its non-trivial zeros play a central role, it is amusing to consider the implications of the Riemann Hypothesis in light of it. |
| title | Phenomenological formula for Quantum Hall resistivity based on the Riemann zeta function |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2209.07468 |