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}
}