## Quantum Wires with Magnetic Fluxes

by
Vadim Kostrykin
,
Robert Schrader

Venue: | Comm. Math. Phys |

Citations: | 20 - 5 self |

### BibTeX

@ARTICLE{Kostrykin_quantumwires,

author = {Vadim Kostrykin and Robert Schrader},

title = {Quantum Wires with Magnetic Fluxes},

journal = {Comm. Math. Phys},

year = {},

volume = {237},

pages = {1--2}

}

### OpenURL

### 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. 1.