Random Aharonov-Bohm vortices and some funny families of integrals

Abstract

A review of the random magnetic impurity model, introduced in the context of the integer Quantum Hall effect, is presented. It models an electron moving in a plane and coupled to random Aharonov-Bohm vortices carrying a fraction of the quantum of flux. Recent results on its perturbative expansion are given. In particular, some funny families of integrals show up to be related to the Riemann $\zeta (3)$ and $\zeta (2)$.

arXiv comment10 pages

References in corpus (2)

• Random Magnetic Impurities and the Landau Problem
• Quantum Mechanics of a Particle with Two Magnetic Impurities

Cited by in corpus (6)

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• Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
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• Aharonov-Bohm effect with many vortices
• Random Aharonov-Bohm vortices and some exact families of integrals: Part II