{"paper":{"title":"Multifractality of wave functions on a Cayley tree: From root to leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"A. D. Mirlin, K. S. Tikhonov, M. Sonner","submitted_at":"2017-08-16T17:10:55Z","abstract_excerpt":"We explore the evolution of wave-function statistics on a finite Bethe lattice (Cayley tree) from the central site (\"root\") to the boundary (\"leaves\"). We show that the eigenfunction moments $P_q=N \\left<|\\psi|^{2q}(i)\\right>$ exhibit a multifractal scaling $P_q\\propto N^{-\\tau_q}$ with the volume (number of sites) $N$ at $N\\to\\infty$. The multifractality spectrum $\\tau_q$ depends on the strength of disorder and on the parameter $s$ characterizing the position of the observation point $i$ on the lattice. Specifically, $s= r/R$, where $r$ is the distance from the observation point to the root, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04978","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"}