Random Aharonov-Bohm vortices and some funny families of integrals

TL;DR

This paper reviews a model of electrons influenced by random magnetic vortices, revealing intriguing integral families connected to special values of the Riemann zeta function, with recent perturbative results discussed.

Contribution

It introduces and analyzes the random magnetic impurity model, highlighting novel integral families linked to Riemann zeta values and providing recent perturbative expansion results.

Findings

Integral families related to Riemann zeta(3) and zeta(2)

Perturbative expansion results for the model

Connection between integrals and quantum Hall effect

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 $\zeta(2)$.