English

Quantum wires with magnetic fluxes

Mathematical Physics 2007-05-23 v2 math.MP

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.

Cite

@article{arxiv.math-ph/0212001,
  title  = {Quantum wires with magnetic fluxes},
  author = {Vadim Kostrykin and Robert Schrader},
  journal= {arXiv preprint arXiv:math-ph/0212001},
  year   = {2007}
}
R2 v1 2026-07-22T16:22:16.619Z