{"paper":{"title":"Inversion Problems for Fourier Transforms of Particle Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Frank H. Stillinger, Ge Zhang, Jaeuk Kim, Salvatore Torquato","submitted_at":"2018-07-06T03:05:09Z","abstract_excerpt":"Collective coordinates in a many-particle system are complex Fourier components of the particle density, and often provide useful physical insights. However, given collective coordinates, it is desirable to infer the particle coordinates via inverse transformations. In principle, a sufficiently large set of collective coordinates are equivalent to particle coordinates, but the nonlinear relation between collective and particle coordinates makes the inversion procedure highly nontrivial. Given a \"target\" configuration in one-dimensional Euclidean space, we investigate the minimal set of its col"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02231","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"}