Wave Vector Dependent Susceptibility of a Free Electron Gas in D Dimensions and the Singularity at 2kF.

Abstract

The static susceptibility of a free electron gas in D dimensions at T = O is obtained by techniques of dimensional regularization. Our solutions for the susceptibility chi(k,D) are given in terms of the hypergeometric function. For any integer solutions analytic expressions are possible. The high and low k series are shown to be related if D is an even integer. The singularity at 2k sub f is a branch point, whereupon the series solutions are absolutely convergent, yielding ( k = 2k sub F,D) = (D-1)-1. The relationship of chi kd has the appearance of a pvt diagram. Keywords: Free electron gas; Susceptibility; and Dimensional Regularization; Hypergeometric Function; Singularity.

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Document Details

Document Type
Technical Report
Publication Date
Apr 02, 1986
Accession Number
ADA166725

Entities

People

  • M. H. Lee
  • N. L. Sharma

Organizations

  • University of Georgia

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Analytic Functions
  • Boundaries
  • Complex Variables
  • Diagrams
  • Electron Gas
  • Electrons
  • Fermions
  • Free Electrons
  • Hypergeometric Functions
  • Military Research
  • Particle Physics
  • Physics
  • Square Roots
  • Subatomic Particles
  • Three Dimensional
  • United States
  • Universities

Readers

  • Analytical Mechanics
  • Calculus or Mathematical Analysis
  • Materials Science and Engineering.

Technology Areas

  • Microelectronics