{"paper":{"title":"Ergodic properties of heterogeneous diffusion processes in a potential well","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Weihua Deng, Xudong Wang, Yao Chen","submitted_at":"2019-01-29T12:48:14Z","abstract_excerpt":"Heterogeneous diffusion processes can be well described by an overdamped Langevin equation with space-dependent diffusivity $D(x)$. We investigate the ergodic and non-ergodic behavior of these processes in an arbitrary potential well $U(x)$ in terms of the observable---occupation time. Since our main concern is the large-$x$ behavior for long times, the diffusivity and potential are, respectively, assumed as the power-law forms $D(x)=D_0|x|^\\alpha$ and $U(x)=U_0|x|^\\beta$ for simplicity. Based on the competition roles played by $D(x)$ and $U(x)$, three different cases, $\\beta>\\alpha$, $\\beta=\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10857","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"}