{"paper":{"title":"One-dimensional disordered quantum mechanics and Sinai diffusion with random absorbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Aur\\'elien Grabsch, Christophe Texier, Yves Tourigny","submitted_at":"2013-10-24T08:06:43Z","abstract_excerpt":"We study the one-dimensional Schr\\\"odinger equation with a disordered potential of the form $V (x) = \\phi(x)^2+\\phi'(x) + \\kappa(x) $ where $\\phi(x)$ is a Gaussian white noise with mean $\\mu g$ and variance $g$, and $\\kappa(x)$ is a random superposition of delta functions distributed uniformly on the real line with mean density $\\rho$ and mean strength $v$. Our study is motivated by the close connection between this problem and classical diffusion in a random environment (the Sinai problem) in the presence of random absorbers~: $\\phi(x)$ models the force field acting on the diffusing particle "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6519","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"}