2002/12/31 by Vadim Kostrykin, Robert Schrader · 3 citations
Mathematics · Physics and Astronomy · #Quantum and electron transport phenomena #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena #math-ph #math.MP #msc:34B45 #msc:34L40 #msc:35J10
paper · pdf · doi:10.1007/s00220-003-0831-7
published as Comm. Math. Phys. 237 (2003), 161 - 179
arxiv created 2003/04/15 · openalex publication_date 2003/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In the present article magnetic Laplacians on a graph are analyzed. We provide a complete description of the set of all operators which can be obtained from a given self-adjoint Laplacian by perturbing it by magnetic fields. In particular, it is shown that generically this set is isomorphic to a torus. We also describe the conditions under which the operator is unambiguously (up to unitary equivalence) defined by prescribing the magnetic fluxes through all loops of the graph.