A rigorous approach to the magnetic response in disordered systems

TL;DR

This paper rigorously establishes the existence and explicit form of thermodynamic limits for magnetic properties of a 3D quantum gas with disorder, covering various physically relevant random potentials.

Contribution

It provides a rigorous proof of the thermodynamic limits and explicit formulas for magnetic response in disordered quantum gases, extending understanding to a broad class of potentials.

Findings

Existence of almost-sure non-random thermodynamic limits

Explicit formulas for pressure, magnetization, and susceptibility

Applicability to crystalline and amorphous disordered solids

Abstract

This paper is a part of an ongoing study on the diamagnetic behavior of a 3-dimensional quantum gas of non-interacting charged particles subjected to an external uniform magnetic field together with a random electric potential. We prove the existence of an almost-sure non-random thermodynamic limit for the grand-canonical pressure, magnetization and zero- field orbital magnetic susceptibility. We also give an explicit formulation of these thermodynamic limits. Our results cover a wide class of physically relevant random potentials which model not only crystalline disordered solids, but also amorphous solids.