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6 "drude"-- Electric and Magnetic Field Response of a Classical Electron Gas







"drude" simulates, in two dimensions, the Drude model for electron transport. Trajectories of an ensemble of electrons in both real and velocity (momentum) space are displayed. A DC magnetic field may be applied perpendicular to the plane of motion and an electric field, either DC or AC, applied in the plane. The temperature of the Maxwell-Boltzmann equilibrium distribution and the relaxation time may also be varied.



The first movie shows the trajectories in real space of 8 electrons, in response to crossed electric (horizontal) and magnetic (perpendicular to the screen) fields. The electrons' positions are left on the screen for five successive cycles of the simulation in order to give a sense of the directions of the trajectories. Follow the trajectory of a single electron to see the characteristic cycloidal motion. If you watch the right-hand one of the two yellow electrons, you see the direction of its motion change discontinuously as it undergoes a scattering event. Note that the left-hand yellow electron moves with nearly constant velocity. What is the value of that velocity in terms of E and B? The large green dot is the center of charge of the distribution. It drifts down, perpendicular to the applied electric field, in this case of infrequent scattering of the electrons. Note that, apart from small fluctuations because of the small number of electrons, there is no hint of the complex cycloidal motion in the motion of the center of charge.



The second clip shows a similar situation but now in velocity space. Here the orbits are simply circles centered on the velocity Vy = -Ex/(Bz*c). (The large red dot is at the origin of velocity space.) Now a scattering event (watch either the red or the green electron) moves the electron discontinously from one point in velocity space to another.











If a circularly polarized electric field oscillates at the frequency of the cyclotron motion of the electrons, it drives the electrons to large amplitude orbits. This is the phenomenon of cyclotron resonance. In the third movie the direction of the electric field is indicated by the short red line at the top of the screen, and again we're seeing five successive velocities of each of 8 electrons. The resonance condition is satisfied here and the electrons are driven in outwardly spiraling orbits. You will see occasional scattering events in which electrons are returned to near the origin of velocity space, the large red dot.











An experimental GIF animation shows a lawn sprinkler (or is it a spider starfish?). The effect is an artifact of the display, in which the animation rate is roughly five frames per cyclotron period, and each electron is shown in five successive positions. (It was too much fun to throw away: it even has some concealed physics in it.)










Table of contents for Chapter 6 of "Simulations for Solid State Physics"
  1. Introduction
  2. No applied fields
    1. Velocity and real space
    2. Diffusion
  3. Electric field (DC)
    1. Drift velocity
    2. Approach to steady state
  4. Noise*
    1. Johnson noise*
    2. Statistical noise*
  5. Magnetic field
    1. Circular orbits
    2. Cyclotron frequency
  6. Crossed fields
    1. Velocity space orbits
    2. Real space orbits
    3. Drift velocity and Hall effect*
    4. Tensor conductivity**
  7. AC Electric field
    1. Zero magnetic field
    2. Cyclotron resonance*
  8. Summary
  9. Appendix: "drude" -- the program

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