Relativistic Characteristics of Electrons in Simple Nonparabolic Energy Bands

Abstract

An analogy is traced between a gas of electrons moving with relativistic velocities and a gas of nonrelativistically moving electrons in simple nonparabolic energy bands.

The works of Herbert Fröhlich have a width and depth that have been an inspiration to younger colleagues like myself. It is appropriate, therefore, for an occasion that honors him to pull out of the bank of models in theoretical physics two items from completely disparate areas, and show that they are basically identical in mathematical structure. The fields are special relativity theory and solid state theory. The analogy to be discussed is an accident without profound and deep implications. However, the facts to be shown up are surprising and they can be suggestive. They enable experiments, that have heretofore been considered appropriate to a relativistic plasma to be transferred to a solid state setting, or vice versa, and the same applies to the mathematical techniques involved (Zawadski et al. 1985; Paverman and Papuashvili, 1985; Landsberg, 1986).