{"paper":{"title":"Class of solvable reaction-diffusion processes on Cayley tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"M. Alimohammadi, N. Olanj","submitted_at":"2009-04-06T05:29:48Z","abstract_excerpt":"Considering the most general one-species reaction-diffusion processes on a Cayley tree, it has been shown that there exist two integrable models. In the first model, the reactions are the various creation processes, i.e. $\\circ\\circ\\to\\bullet\\circ$, $\\circ\\circ\\to\\bullet\\bullet$ and $\\circ\\bullet\\to\\bullet\\bullet$, and in the second model, only the diffusion process $\\bullet\\circ\\to\\circ\\bullet$ exists. For the first model, the probabilities $P_l(m;t)$, of finding $m$ particles on $l$-th shell of Cayley tree, have been found exactly, and for the second model, the functions $P_l(1;t)$ have been"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0847","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"}