Passive Quasi-Free States of the Noninteracting Fermi Gas

Abstract

The passive quasi-free states of the noninteracting Fermi gas with continuous one-particle Hamiltonian H are computed. They turn out to be the well known Fermi-Dirac states, or limits thereof. This still holds true if the spectrum of H has both a continuous and a discrete part, except for the appearance of a class of "ground state-like" states showing a local random excitation of the point spectrum in a neighborhood of the Fermi energy. When H has only pure point spectrum, the requirement that a state be passive and quasi-free is no longer sufficient to characterize the Fermi-Dirac distributions.