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Random Aharonov-Bohm vortices and some funny families of integrals

Stephane Ouvry
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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 $ζ(3)$ and $ζ(2)$.

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Stephane Ouvry. 2005-02-15. Random Aharonov-Bohm vortices and some funny families of integrals. https://doi.org/10.1088/1742-5468%2F2005%2F09%2Fp09004

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