{"paper":{"title":"Non-affine displacements in crystalline solids in the harmonic limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.stat-mech","authors_text":"Madan Rao, Peter Sollich, Saswati Ganguly, Surajit Sengupta","submitted_at":"2012-12-27T14:35:47Z","abstract_excerpt":"A systematic coarse graining of microscopic atomic displacements generates a local elastic deformation tensor ${\\mathsf D}$ as well as a positive definite scalar $\\chi$ measuring non-affinity, i.e. the extent to which the displacements are not representable as affine deformations of a reference crystal. We perform an exact calculation of the statistics of $\\chi$ and ${\\mathsf D}$ and their spatial correlations for solids at low temperatures, within a harmonic approximation and in one and two dimensions. We obtain the joint distribution $P(\\chi, {\\mathsf D})$ and the two point spatial correlati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6377","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"}