Drude model electron interaction

In summary, physicists convinced themselves that electron-electron interactions could be neglected in the Drude model through the Landau Fermi liquid theory, which showed that these interactions can only be ignored near the Fermi surface. This theory also demonstrates that there is still a Fermi surface when these interactions are accounted for.
  • #1
charbon
23
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In every source I've checked so far, we make the assumption that we can neglect electron-electron interaction in this model but they always fail to give any reason to answer why this is plausible. Does anyone know how physicists convinced themselves of this at the time and even now (other than the fact that it just works of course!)?
 
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  • #2
The model that Drude originally proposed was a lot crazier than what is now usually meant by "Drude's model". In it, "electrons" were both positive and negative, plus they could carry a multiple of elementary charge e. Oh, and they did not have any mass (but they had an "apparent mass"). He then said that the question why those "electrons" don't get stuck together and form "neutral aether-points" "explains itself" once the kinetic energy of the "electrons" exceeds some certain level. The collisions between them were what determined their mean free path, on which the entire theory hinges.
 
  • #3
charbon said:
In every source I've checked so far, we make the assumption that we can neglect electron-electron interaction in this model but they always fail to give any reason to answer why this is plausible. Does anyone know how physicists convinced themselves of this at the time and even now (other than the fact that it just works of course!)?

The answer is known under the name "Landau fermi liquid theory":
http://en.wikipedia.org/wiki/Fermi_liquid_theory

Basically, electron-electron collisions can only be neglected in a small region around the Fermi surface due. For these electrons, momentum conservation and Pauli principle prohibits scattering.
The difficult part is to show that, if electron-electron interactions are taken into account, there is still a Fermi surface.
 

1. What is the Drude model of electron interaction?

The Drude model is a theoretical model used to describe the behavior of electrons in a metal. It assumes that the electrons move freely through the metal and are subject to collisions with the metal ions, resulting in a net resistance to the flow of electrons.

2. What are the main assumptions of the Drude model?

The Drude model assumes that the electrons in a metal are free to move and are subject to collisions with the metal ions. It also assumes that these collisions are the primary source of resistance in the metal and that the electrons have a constant average velocity between collisions.

3. How does the Drude model explain electrical conductivity in metals?

The Drude model explains electrical conductivity in metals by describing how the free electrons move through the metal and interact with the metal ions. When an electric field is applied, the electrons gain a net drift velocity, resulting in a flow of current. The collisions with metal ions impede the movement of the electrons, resulting in resistance and a decrease in the net current.

4. What are the limitations of the Drude model?

The Drude model has several limitations, including the assumption that the electrons are free to move and that the collisions with metal ions are the only source of resistance. It also does not take into account the quantum nature of electrons and does not accurately describe the behavior of electrons at very low temperatures.

5. How does the Drude model relate to other models of electron interaction?

The Drude model is a simplified version of more advanced models, such as the quantum mechanical model and the band theory model. It is often used as a starting point for understanding electron behavior in metals and can be extended to include more complex factors, such as the effects of temperature and impurities.

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