Minimization of the discrete interaction energy with smooth potentials
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910727172784128 |
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| author | Almog, Yaniv |
| author_facet | Almog, Yaniv |
| contents | We study the pair interaction on flat tori of functions whose Fourier coefficients are positive and decay sufficiently rapidly. In dimension one we find that the minimizer, up to translation, is the equidistant point set. In dimension two, minimizing with respect to triplets we find that the minimizer is the triangular lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03425 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimization of the discrete interaction energy with smooth potentials Almog, Yaniv Mathematical Physics 52C35, 52C99, 42A16 We study the pair interaction on flat tori of functions whose Fourier coefficients are positive and decay sufficiently rapidly. In dimension one we find that the minimizer, up to translation, is the equidistant point set. In dimension two, minimizing with respect to triplets we find that the minimizer is the triangular lattice. |
| title | Minimization of the discrete interaction energy with smooth potentials |
| topic | Mathematical Physics 52C35, 52C99, 42A16 |
| url | https://arxiv.org/abs/2412.03425 |