Real-Analyticity of the Density of States for Random Schrödinger operators with Point Interactions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918126530068480 |
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| author | Kaminaga, Masahiro |
| author_facet | Kaminaga, Masahiro |
| contents | We prove real-analyticity of the density of states (DOS) for random Schrödinger operators with lattice-supported point interactions in $\mathbb{R}^d$ ($d=1,2,3$) in the small-hopping regime. In the attractive case, Krein's resolvent formula reduces the problem to a lattice model, where a random-walk expansion and disorder averaging lead to single-site integrals with holomorphic single-site density $g$. Contour deformation in the coupling-constant plane under a uniform pole-gap condition ensures convergence of the averaged resolvent in a complex neighborhood of a negative-energy interval. This yields analyticity of the DOS. The method also applies to multi-point correlation functions, such as those in the Kubo--Greenwood formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Real-Analyticity of the Density of States for Random Schrödinger operators with Point Interactions Kaminaga, Masahiro Mathematical Physics We prove real-analyticity of the density of states (DOS) for random Schrödinger operators with lattice-supported point interactions in $\mathbb{R}^d$ ($d=1,2,3$) in the small-hopping regime. In the attractive case, Krein's resolvent formula reduces the problem to a lattice model, where a random-walk expansion and disorder averaging lead to single-site integrals with holomorphic single-site density $g$. Contour deformation in the coupling-constant plane under a uniform pole-gap condition ensures convergence of the averaged resolvent in a complex neighborhood of a negative-energy interval. This yields analyticity of the DOS. The method also applies to multi-point correlation functions, such as those in the Kubo--Greenwood formula. |
| title | Real-Analyticity of the Density of States for Random Schrödinger operators with Point Interactions |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2508.12664 |