Three-dimensional magnetic Schrödinger operator with the potential supported in a tube
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916770221129728 |
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| author | Barseghyan, Diana Bory-Reyes, Juan Schneider, Baruch |
| author_facet | Barseghyan, Diana Bory-Reyes, Juan Schneider, Baruch |
| contents | In this paper, we study the following magnetic Schrödinger operator in $\mathbb{R}^3$: \[ H=(i \nabla +A)^2- \tilde{V}, \] where $\tilde{V}$ is non-negative potential supported over the tube built along a curve which is a local deformation of a straight one, and $B:=\mathrm{rot}(A)$ is a non-zero and local (i.e., a compact supported) magnetic field. Based on some new strategies, we first prove that the magnetic field does not change the essential spectrum of this system. Finally, in the last section of this paper, we establish the sufficient condition such that the discrete spectrum is empty. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_19365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three-dimensional magnetic Schrödinger operator with the potential supported in a tube Barseghyan, Diana Bory-Reyes, Juan Schneider, Baruch Spectral Theory Mathematical Physics In this paper, we study the following magnetic Schrödinger operator in $\mathbb{R}^3$: \[ H=(i \nabla +A)^2- \tilde{V}, \] where $\tilde{V}$ is non-negative potential supported over the tube built along a curve which is a local deformation of a straight one, and $B:=\mathrm{rot}(A)$ is a non-zero and local (i.e., a compact supported) magnetic field. Based on some new strategies, we first prove that the magnetic field does not change the essential spectrum of this system. Finally, in the last section of this paper, we establish the sufficient condition such that the discrete spectrum is empty. |
| title | Three-dimensional magnetic Schrödinger operator with the potential supported in a tube |
| topic | Spectral Theory Mathematical Physics |
| url | https://arxiv.org/abs/2505.19365 |