{"paper":{"title":"Spectral shift function for slowly varying perturbation of periodic Schroedinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Maher Zerzeri, Mouez Dimassi","submitted_at":"2011-02-11T14:41:38Z","abstract_excerpt":"In this paper we study the asymptotic expansion of the spectral shift function for the slowly varying perturbations of periodic Schr\\\"odinger operators. We give a weak and pointwise asymptotics expansions in powers of $h$ of the derivative of the spectral shift function corresponding to the pair $\\big(P(h)=P_0+\\phi(hx),P_0=-\\Delta+V(x)\\big),$ where $\\phi(x)\\in {\\mathcal C}^\\infty(\\mathbb R^n,\\mathbb R)$ is a decreasing function, ${\\mathcal O}(|x|^{-\\delta})$ for some $\\delta>n$ and $h$ is a small positive parameter. Here the potential $V$ is real, smooth and periodic with respect to a lattice "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2362","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"}