{"paper":{"title":"Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"cond-mat.stat-mech","authors_text":"Aleksei V. Chechkin, Andrey G. Cherstvy, Ralf Metzler","submitted_at":"2013-03-22T07:21:30Z","abstract_excerpt":"We demonstrate the non-ergodicity of a simple Markovian stochastic processes with space-dependent diffusion coefficient $D(x)$. For power-law forms $D(x) \\simeq|x|^{\\alpha}$, this process yield anomalous diffusion of the form $\\ < x^2(t)\\ > \\simeq t^{2/(2-\\alpha)}$. Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time averaged mean squared displacement $\\{\\delta^2}$ remains \\emph{linear} and thus differs from the corresponding ensemble average $\\ <x^2(t)\\ >$. We analyze the non-ergodic behavior of this process in terms of the e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5533","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"}