On the spectrum of the Landau Hamiltonian perturbed by a periodic electric potential $V\in H^s_{\mathrm {loc}}({\mathbb R}^2;{\mathbb R})$, $s > 0$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910743001038848 |
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| author | Danilov, L. I. |
| author_facet | Danilov, L. I. |
| contents | We prove that in a Sobolev space $H^s_{Λ}({\mathbb R}^2;{\mathbb R})$, $s > 0$, of periodic functions with a given period lattice $Λ$, there exists a dense $G_{δ}$-set ${\mathcal O}$ such that the spectrum of the Landau Hamiltonian $H_B + V$ perturbed by any periodic electric potential $V\in {\mathcal O}$ is absolutely continuous for all homogeneous magnetic fields with a rational flux. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the spectrum of the Landau Hamiltonian perturbed by a periodic electric potential $V\in H^s_{\mathrm {loc}}({\mathbb R}^2;{\mathbb R})$, $s > 0$ Danilov, L. I. Mathematical Physics Spectral Theory 35P05 We prove that in a Sobolev space $H^s_{Λ}({\mathbb R}^2;{\mathbb R})$, $s > 0$, of periodic functions with a given period lattice $Λ$, there exists a dense $G_{δ}$-set ${\mathcal O}$ such that the spectrum of the Landau Hamiltonian $H_B + V$ perturbed by any periodic electric potential $V\in {\mathcal O}$ is absolutely continuous for all homogeneous magnetic fields with a rational flux. |
| title | On the spectrum of the Landau Hamiltonian perturbed by a periodic electric potential $V\in H^s_{\mathrm {loc}}({\mathbb R}^2;{\mathbb R})$, $s > 0$ |
| topic | Mathematical Physics Spectral Theory 35P05 |
| url | https://arxiv.org/abs/2412.09212 |