# Random Aharonov-Bohm vortices and some exactly solvable 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 $\\zeta(2)$.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00011181
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Submitted on : Wednesday, October 12, 2005 - 3:28:17 PM
Last modification on : Thursday, October 7, 2021 - 3:37:27 AM

### Citation

Stephane Ouvry. Random Aharonov-Bohm vortices and some exactly solvable families of integrals. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2005, 1, pp.P09004. ⟨hal-00011181⟩

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