02-507 Vadim Kostrykin and Robert Schrader

Quantum wires with magnetic fluxes (60K, LaTeX2e) Dec 7, 02

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Abstract. 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.

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