{"paper":{"title":"Hofstadter Rules and Generalized Dimensions of the Spectrum of Harper's Equation","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Andreas Rudinger, Frederic Piechon","submitted_at":"1996-10-24T13:34:46Z","abstract_excerpt":"We consider the Harper model which describes two dimensional Bloch electrons in a magnetic field. For irrational flux through the unit-cell the corresponding energy spectrum is known to be a Cantor set with multifractal properties. In order to relate the maximal and minimal fractal dimension of the spectrum of Harper's equation to the irrational number involved, we combine a refined version of the Hofstadter rules with results from semiclassical analysis and tunneling in phase space. For quadratic irrationals $\\omega$ with continued fraction expansion $\\omega = [0;\\overline{n}]$ the maximal fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9610177","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"}