{"paper":{"title":"Some properties of the one-dimensional L\\'{e}vy crystal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"B.A. Stickler","submitted_at":"2013-06-25T08:23:11Z","abstract_excerpt":"We introduce and discuss the one-dimensional L\\'{e}vy crystal as a probable candidate for an experimentally accessible realization of space fractional quantum mechanics (SFQM) in a condensed matter environment. The discretization of the space fractional Schr\\\"{o}dinger equation with the help of shifted Gr\\\"{u}nwald-Letnikov derivatives delivers a straight-forward route to define the L\\'{e}vy crystal of order $\\alpha \\in (1,2]$. As key ingredients for its experimental identification we study the dispersion relation as well as the density of states for arbitrary $\\alpha \\in (1,2]$. It is demonst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5874","kind":"arxiv","version":2},"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"}