{"paper":{"title":"Spectral properties of Landau Hamiltonians with non-local potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Esteban C\\'ardenas, Georgi Raikov, Ignacio Tejeda","submitted_at":"2019-01-14T16:03:36Z","abstract_excerpt":"We consider the Landau Hamiltonian $H_0$, self-adjoint in $L^2({\\mathbb R^2})$, whose spectrum consists of an arithmetic progression of infinitely degenerate positive eigenvalues $\\Lambda_q$, $q \\in {\\mathbb Z}_+$. We perturb $H_0$ by a non-local potential written as a bounded pseudo-differential operator ${\\rm Op}^{\\rm w}({\\mathcal V})$ with real-valued Weyl symbol ${\\mathcal V}$, such that ${\\rm Op}^{\\rm w}({\\mathcal V}) H_0^{-1}$ is compact. We study the spectral properties of the perturbed operator $H_{{\\mathcal V}} = H_0 + {\\rm Op}^{\\rm w}({\\mathcal V})$. First, we construct symbols ${\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04370","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"}