{"paper":{"title":"Dynamical properties of random Schr\\\"odinger operators","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jean-Marie Barbaroux, Peter M\\\"uller, Werner Fischer","submitted_at":"1999-07-01T17:36:10Z","abstract_excerpt":"We study dynamical properties of random Schr\\\"odinger operators $H^{(\\omega)}$ defined on the Hilbert space $\\ell^2(\\bbZ^d)$ or $L^2(\\bbR^d)$. Building on results from existing multi-scale analyses, we give sufficient conditions on $H^{(\\omega)}$ to obtain the vanishing of the diffusion exponent $$\n \\sigma_{\\rm diff}^+ := \\limsup_{T\\rightarrow\\infty } \\frac{\\log\n  \\bbE \\left(\\la\\la\\vert X\n  \\vert^2\\ra\\ra_{T,f_I(H^{(\\omega)})\\psi}\\right) }{\\log T}=0. $$ Here $\\bbE$ is the expectation over randomness, $f_{I}$ is any smooth characteristic function of a bounded energy-interval $I$ and $\\psi$ is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9907002","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"}