Asymptotic Exactness of Magnetic Thomas-Fermi Theory

TL;DR

This paper proves that the grand canonical pressure for Coulombic matter in a magnetic field converges asymptotically to a Thomas-Fermi type functional as nuclear charge increases, under specific magnetic field conditions.

Contribution

It establishes the asymptotic exactness of magnetic Thomas-Fermi theory for Coulombic matter in the large nuclear charge limit with weak magnetic fields.

Findings

Asymptotic limit of pressure matches Thomas-Fermi functional

Validates magnetic Thomas-Fermi theory in specified regime

Provides rigorous mathematical proof for the limit

Abstract

We consider the grand canonical pressure for Coulombic matter with nuclear charges $\sim Z$ in a magnetic field $B$ and at nonzero temperature. We prove that its asymptotic limit as $Z\to\infty$ with $B/Z^3\to 0$ can be obtained by minimizing a Thomas-Fermi type pressure functional.