Number Theory and the Magnetic Properties of an Electron Gas

Abstract

Theorems involving the correction terms of lattice point problems in the theory of numbers are interpreted to derive the orders of magnitude of the oscillatory (de Haas-van Alphen effect) and non-oscillatory (Landau and surface diamagnetism) terms in the magnetic moment of a Fermi gas in a finite cylindrical container. The results are valid for systems from atomic dimensions up, and all values of the magnetic field. The different types of moment are different from strong and weak fields, and may depend, for small particles, on the nature of the surface potential at the walls of the container. The applicability of the method to physical problems, and the difficulties associated with statistical mechanical problems involving magnetic fields are discussed.