{"paper":{"title":"Spectral shift function for perturbed periodic Schroedinger operators. The large-coupling constant limit case","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":"2011-02-11T14:53:20Z","abstract_excerpt":"In the large coupling constant limit, we obtain an asymptotic expansion in powers of $\\mu^{-\\frac{1}{\\delta}}$ of the derivative of the spectral shift function corresponding to the pair $\\big(P_\\mu=P_0+\\mu W(x),P_0=-\\Delta+V(x)\\big),$ where $W(x)$ is positive, $W(x)\\sim w_0(\\frac{x}{|x|})|x|^{-\\delta}$ near infinity for some $\\delta>n$ and $w_0\\in {\\mathcal C}^\\infty(\\mathbb S^{n-1};\\,\\mathbb R_+).$ Here $\\mathbb S^{n-1}$ is the unite sphere of the space $\\mathbb R^n$ and $\\mu$ is a large parameter. The potential $V$ is real-valued, smooth and periodic with respect to a lattice $\\Gamma$ in ${\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2364","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"}