{"paper":{"title":"Multifractal dimensions for critical random matrix ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"A. Alcazar-Lopez, Imre Varga, J. A. Mendez-Bermudez","submitted_at":"2012-01-30T20:55:49Z","abstract_excerpt":"Based on heuristic arguments we conjecture that an intimate relation exists between the eigenfunction multifractal dimensions $D_q$ of the eigenstates of critical random matrix ensembles $D_{q'} \\approx qD_q[q'+(q-q')D_q]^{-1}$, $1\\le q \\le 2$. We verify this relation by extensive numerical calculations. We also demonstrate that the level compressibility $\\chi$ describing level correlations can be related to $D_q$ in a unified way as $D_q=(1-\\chi)[1+(q-1)\\chi]^{-1}$, thus generalizing existing relations with relevance to the disorder driven Anderson--transition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6353","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"}