Faraday effect revisited: sum rules and convergence issues

Abstract

This is the third paper of a series revisiting the Faraday effect. The question of the absolute convergence of the sums over the band indices entering the Verdet constant is considered. In general, sum rules and traces per unit volume play an important role in solid state physics, and they give rise to certain convergence problems widely ignored by physicists. We give a complete answer in the case of smooth potentials and formulate an open problem related to less regular perturbations.

Dedicated to the memory of our late friend Pierre Duclos. Accepted for publication in Journal of Physics A: Mathematical and Theoretical.

References in corpus (8)

• The Magnetic Weyl Calculus
• Magnetic Pseudodifferential Operators
• The Faraday effect revisited: Thermodynamic limit
• The Faraday effect revisited: General theory
• Strict Deformation Quantization for a Particle in a Magnetic Field
• Optical second harmonic generation from Wannier excitons
• On the Magnetization of a Charged Bose Gas in the Canonical Ensemble
• Spectral and Propagation Results for Magnetic Schroedinger Operators; a C*-Algebraic Framework

Cited by in corpus (2)

• On the zero-field orbital magnetic susceptibility of Bloch electrons in graphene-like solids: Some rigorous results
• Gauge-invariant perturbation expansion in powers of electric charge for the density-of-states of a network model for charged-particle motion in a uniform background magnetic flux density