{"paper":{"title":"Surface Lifshits tails for random quantum Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Georgi Raikov, Werner Kirsch","submitted_at":"2016-02-16T18:26:37Z","abstract_excerpt":"We consider Schr\\\"{o}dinger operators on $L^{2}({\\mathbb R}^{d})\\otimes L^{2}({\\mathbb R}^{\\ell})$ of the form $ H_{\\omega}~=~H_{\\perp}\\otimes I_{\\parallel} + I_{\\perp} \\otimes {H_\\parallel} + V_{\\omega}$, where $H_{\\perp}$ and $H_{\\parallel}$ are Schr\\\"{o}dinger operators on $L^{2}({\\mathbb R}^{d})$ and $L^{2}({\\mathbb R}^{\\ell})$ respectively, and $ V_\\omega(x,y)$ : = $\\sum_{\\xi \\in {\\mathbb Z}^{d}} \\lambda_\\xi(\\omega) v(x - \\xi, y)$, $x \\in {\\mathbb R}^d$, $y \\in {\\mathbb R}^\\ell$, is a random 'surface potential'. We investigate the behavior of the integrated density of surface states of $H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05123","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"}