Random Aharonov-Bohm vortices and some exactly solvable families of integrals

Stephane Ouvry 1

Journal of Statistical Mechanics: Theory and Experiment 1 (2005) P09004

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 $\\zeta(2)$.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud