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7 "sommerfeld" - response of a degenerate gas of free electrons

"sommerfeld" explores the dynamics of the degenerate electron gas in electric and magnetic fields. The animation display shows the momentum (k) space trajectories of individual electrons as well as the average crystal-momentum of the ensemble. A model is adopted which incorporates the exclusion principle into the scattering and the scattering may be chosen to be an arbitrary mixture of elastic and inelastic. The time dependence of the average wave vector is displayed graphically.

The left display shows the distribution in velocity space of the occupied electron states of a Sommerfeld electron gas. An electric field is applied in the positive x-direction and a magnetic field is perpendicular to the plane of the screen. The green dot is the average velocity of all of the elctrons and is displaced from the origin (possibly visible as a red dot) to the left and roughly 30 degrees below the horizontal. This angle is the Hall angle. The average velocity versus time is displayed in the graph: the x-velocity in blue, the y-velocity in green, The electric field was applied at time t=0, with the system initially in equilibrium. In the initial transient, why does the x-component of the current build up faster than the y-component?
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Table of contents for Chapter 7 of Simulations for Solid State Physics
  1. Introduction
  2. Ground state
    1. One-electron states
    2. Fermi sphere
    3. Thermal energies
  3. Electric field
    1. Exclusion principle
    2. Displaced Fermi sea
    3. Distribution function**
  4. Crossed E and B fields
  5. Heating of the electron gas*
  6. Summary
  7. Appendix: "sommerfeld" -- the program
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