Taming of the wild group of magnetic translations

TL;DR

This paper investigates the representation theory of magnetic translation groups in quasi-periodic systems, demonstrating that these groups are of Type I when magnetic fields fluctuate, using advanced Lie-group theorems.

Contribution

It applies Auslandar and Kostant's theorem to show magnetic translation groups are tame under fluctuating magnetic fields, a novel insight in solid-state physics.

Findings

Magnetic translation groups are Type I with fluctuating fields.

Representation theory of solvable Lie groups is used.

Results impact understanding of quasi-periodic systems.

Abstract

We use a theorem of Auslander and Kostant on the representation theory of solvable Lie-groups for the study of some groups necessary for the description of certain quasi-periodic systems of solid-state physics. We show that the magnetic translation group is tame (Type I) if the magnetic field is not constant but fluctuating.