Integrated density of states for the Poisson point interactions on $\mathbf{R}^3$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913959353778176 |
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| author | Kaminaga, Masahiro Mine, Takuya Nakano, Fumihiko |
| author_facet | Kaminaga, Masahiro Mine, Takuya Nakano, Fumihiko |
| contents | We determine the principal term of the asymptotics of the integrated density of states (IDS) $N(λ)$ for the Schrödinger operator with point interactions on $\mathbf{R}^3$ as $λ\to -\infty$, provided that the set of positions of the point obstacles is the Poisson configuration, and the interaction parameters are bounded i.i.d.\ random variables. In particular, we prove $N(λ) =O(|λ|^{-3/2})$ as $λ\to -\infty$. In the case that all interaction parameters are equal to a constant, we give a more detailed asymptotics of $N(λ)$, and verify the result by a numerical method using R. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02256 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrated density of states for the Poisson point interactions on $\mathbf{R}^3$ Kaminaga, Masahiro Mine, Takuya Nakano, Fumihiko Mathematical Physics We determine the principal term of the asymptotics of the integrated density of states (IDS) $N(λ)$ for the Schrödinger operator with point interactions on $\mathbf{R}^3$ as $λ\to -\infty$, provided that the set of positions of the point obstacles is the Poisson configuration, and the interaction parameters are bounded i.i.d.\ random variables. In particular, we prove $N(λ) =O(|λ|^{-3/2})$ as $λ\to -\infty$. In the case that all interaction parameters are equal to a constant, we give a more detailed asymptotics of $N(λ)$, and verify the result by a numerical method using R. |
| title | Integrated density of states for the Poisson point interactions on $\mathbf{R}^3$ |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2406.02256 |