{"paper":{"title":"Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Andrzej Nowakowski, Bernard Collet (IJLRA), Franck Nicolleau, Thomas Michelitsch (IJLRA)","submitted_at":"2014-12-18T15:49:48Z","abstract_excerpt":"The 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finitenumber $N$ of identical particles is introduced. We suggest a \"fractional elastic harmonic potential\", and obtain the $N$-periodic fractionalLaplacian operator in the form of a power law matrix function for the finite chain ($N$ arbitrary not necessarily large) in explicit form.In the limiting case $N\\rightarrow \\infty$ this fractional Laplacian matrix recovers the fractional Laplacian matrix ofthe infinite chain.The lattice model contains two free material constants, the particle mass $\\mu$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5904","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}