Discrete versus continuous -- linear lattice models and their exact continuous counterparts
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918384015245312 |
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| author | Fusi, Lorenzo Křenek, Oliver Průša, Vít Rodriguez, Casey Tozzi, Rebecca Vejvoda, Martin |
| author_facet | Fusi, Lorenzo Křenek, Oliver Průša, Vít Rodriguez, Casey Tozzi, Rebecca Vejvoda, Martin |
| contents | We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence problem for linear nearest neighbour interaction lattice models as well as for linear multiple-neighbour interaction lattice models, while we gradually proceed from infinite lattices to periodic lattices and finally to finite lattices with fixed ends/zero Dirichlet boundary conditions. The whole study is framed as a systematic specialisation of Fourier analysis tools from the continuous to the discrete setting and vice versa, and the correspondence between the discrete and continuous models is examined primarily with regard to the dispersion relation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10184 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discrete versus continuous -- linear lattice models and their exact continuous counterparts Fusi, Lorenzo Křenek, Oliver Průša, Vít Rodriguez, Casey Tozzi, Rebecca Vejvoda, Martin Classical Physics Numerical Analysis Computational Physics 74B05, 65M06, 65M70 We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence problem for linear nearest neighbour interaction lattice models as well as for linear multiple-neighbour interaction lattice models, while we gradually proceed from infinite lattices to periodic lattices and finally to finite lattices with fixed ends/zero Dirichlet boundary conditions. The whole study is framed as a systematic specialisation of Fourier analysis tools from the continuous to the discrete setting and vice versa, and the correspondence between the discrete and continuous models is examined primarily with regard to the dispersion relation. |
| title | Discrete versus continuous -- linear lattice models and their exact continuous counterparts |
| topic | Classical Physics Numerical Analysis Computational Physics 74B05, 65M06, 65M70 |
| url | https://arxiv.org/abs/2601.10184 |