Momentum Distributions: An Overview

Abstract

While all systems of classical particles have single-particle momentum distributions n(p) of Maxwell-Boltzmann form, the momentum distribution plays a role central to our understanding of systems of quantum particles. An outstanding example is the low-temperature superfluid behavior of the Bose liquid, 4He, where the superfluidity is associated with Bose condensation of a macroscopic fraction of the 4He atoms into a zero-momentum state. The momentum distribution is complementary to other characterizations of many-body systems and can be more informative. The pair correlation function of liquid 4He is very close to that of a hard-sphere classical fluid, whereas the momentum distribution reveals the quantum behavior in the form of a δ-function spike in n(p) at p = 0 due to the Bose condensate. Momentum distributions are equally fundamental to the description of Fermi systems. The Fermi-liquid properties of 3He and electrons in metals are associated with a discontinuity in the momentum distribution at the Fermi momentum, k F , which defines a Fermi surface for a three-dimensional system. A detailed description of the, often complex, Fermi surfaces in metals is essential to understanding their transport, optical, and magnetic properties. At low temperatures, the transition to superfluid behavior of 3He and the transition to superconducting behavior of electrons is associated with the disappearance of this Fermi surface.