Landau Hamiltonian with Gaussian white noise potential and the asymptotic of its bottom of spectrum
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914172586950656 |
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| author | Hsu, Yueh-Sheng |
| author_facet | Hsu, Yueh-Sheng |
| contents | We present a simple construction of a random Schrödinger operator subject to a magnetic field with a regularity as low as $0^-$-Hölder and a Gaussian white noise electric potential on a two-dimensional bounded box. This construction is based on the exponential Ansatz introduced in [HL15] and leverages the semigroup approach developed in [HL24].
The proposed construction enables us to generalise an asymptotic result for the bottom of the spectrum of the two-dimensional continuous Anderson Hamiltonian, first proved in [CvZ21], to the magnetic case. Our choice of potential not only covers the case of a uniform magnetic field, but also those which would break translational invariance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22162 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Landau Hamiltonian with Gaussian white noise potential and the asymptotic of its bottom of spectrum Hsu, Yueh-Sheng Probability Mathematical Physics Spectral Theory Primary 35J10, 60H15, Secondary 47A10 We present a simple construction of a random Schrödinger operator subject to a magnetic field with a regularity as low as $0^-$-Hölder and a Gaussian white noise electric potential on a two-dimensional bounded box. This construction is based on the exponential Ansatz introduced in [HL15] and leverages the semigroup approach developed in [HL24]. The proposed construction enables us to generalise an asymptotic result for the bottom of the spectrum of the two-dimensional continuous Anderson Hamiltonian, first proved in [CvZ21], to the magnetic case. Our choice of potential not only covers the case of a uniform magnetic field, but also those which would break translational invariance. |
| title | Landau Hamiltonian with Gaussian white noise potential and the asymptotic of its bottom of spectrum |
| topic | Probability Mathematical Physics Spectral Theory Primary 35J10, 60H15, Secondary 47A10 |
| url | https://arxiv.org/abs/2511.22162 |