The Faraday effect revisited: Thermodynamic limit

TL;DR

This paper rigorously establishes the thermodynamic limit for the Faraday effect, specifically the transverse electric conductivity and Verdet constant, using advanced mathematical techniques.

Contribution

It introduces a mathematical framework proving the thermodynamic limit for the Faraday effect's key quantities in Bloch electrons.

Findings

Proved the thermodynamic limit for transverse electric conductivity.

Established the thermodynamic limit for the Verdet constant.

Developed a novel mathematical approach combining perturbation theory and decay estimates.

Abstract

This paper is the second in a series revisiting the (effect of) Faraday rotation. We formulate and prove the thermodynamic limit for the transverse electric conductivity of Bloch electrons, as well as for the Verdet constant. The main mathematical tool is a regularized magnetic and geometric perturbation theory combined with elliptic regularity and Agmon-Combes-Thomas uniform exponential decay estimates.