{"paper":{"title":"The bulk-edge correspondence for continuous dislocated systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexis Drouot","submitted_at":"2018-10-24T20:17:53Z","abstract_excerpt":"We study topological aspects of defect modes for a family of operators $\\{\\mathscr{P}(t)\\}_{t \\in [0,2\\pi]}$ on $L^2(\\mathbb{R})$. $\\mathscr{P}(t)$ is a periodic Schr\\\"odinger operator $P_0$ perturbed by a dislocated potential. This potential is periodic on the left and on the right, but acquires a phase defect $t$ from $-\\infty$ relative to $+\\infty$. When $t=\\pi$ and the dislocation is small and adiabatic, Fefferman, Lee-Thorp and Weinstein showed in previous work that Dirac points of $P_0$ (degeneracies in the band spectrum of $P_0$) bifurcate to defect modes of $\\mathscr{P}(\\pi)$.\n  We sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10603","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"}