## Quantum Wires with Magnetic Fluxes

Venue: | Comm. Math. Phys |

Citations: | 21 - 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.

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Citation Context ...elated to Chern numbers [3], [4], [5], [6]. In the present article we study general differential self-adjoint magnetic Laplacians on finite graphs. This work is a continuation of our previous studies =-=[18]-=-, [19], [20]. We consider an arbitrary nontrivial connected (metrical) graph G with a finite number n # 0 of external lines and a finite number m # 0 of internal lines (henceforth also called edges), ... |

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Citation Context ...Laplacians on finite graphs appear in a number of physical applications. The major interest in operators of this type originates from the study of quantum transport in mesoscopic networks (see, e.g., =-=[1]-=-, [3], [4], [5], [6], [7], [10], [13]). Magnetic Laplacians have also been the subject of several studies in the context of quantum chaos [22], [23], [24]. The most intriguing feature of Laplacians on... |

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