{"paper":{"title":"Spectral problems for operators with crossed magnetic and electric fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Mouez Dimassi, Vesselin Petkov","submitted_at":"2010-06-01T18:04:04Z","abstract_excerpt":"We obtain a representation formula for the derivative of the spectral shift function $\\xi(\\lambda; B, \\epsilon)$ related to the operators $H_0(B,\\epsilon) = (D_x - By)^2 + D_y^2 + \\epsilon x$ and $H(B, \\epsilon) = H_0(B, \\epsilon) + V(x,y), \\: B > 0, \\epsilon > 0$. We prove that the operator $H(B, \\epsilon)$ has at most a finite number of embedded eigenvalues on $\\R$ which is a step to the proof of the conjecture of absence of embedded eigenvalues of $H$ in $\\R.$ Applying the formula for $\\xi'(\\lambda, B, \\epsilon)$, we obtain a semiclassical asymptotics of the spectral shift function related "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0202","kind":"arxiv","version":3},"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"}