Communications in Mathematical Physics

, Volume 237, Issue 1–2, pp 161–179 | Cite as

Quantum Wires with Magnetic Fluxes

  • Vadim Kostrykin
  • Robert Schrader


 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.


Magnetic Field Present Article Magnetic Flux Quantum Wire 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Vadim Kostrykin
    • 1
  • Robert Schrader
    • 2
  1. 1.Fraunhofer-Institut für Lasertechnik, Steinbachstraße 15, 52074 Aachen, Germany. E-mail:; kostrykin@t-online.deDE
  2. 2.Institut für Theoretische Physik Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany. E-mail: schrader@physik.fu-berlin.deDE

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