Drude Model: Electrons & Collisions

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SUMMARY

The Drude model describes electron behavior in a conductor, asserting that electrons move randomly after collisions, with a mean velocity defined by the equation -eEτ/m, where τ is the relaxation time. A participant expressed confusion regarding the assumption of randomness in electron velocity post-collision, questioning the validity of this model when considering interactions between electrons. Additionally, the discussion touches on the equation for the displacement of a Fermi sphere, represented as h(d/dt + 1/τ)δk = F, and seeks clarification on the role of δk in this context.

PREREQUISITES
  • Understanding of the Drude model of electrical conduction
  • Familiarity with concepts of relaxation time (τ) and mean velocity in physics
  • Knowledge of Fermi spheres and their significance in solid-state physics
  • Basic grasp of quantum mechanics, particularly the role of hbar (ħ) in equations
NEXT STEPS
  • Research the implications of the Drude model on electrical conductivity in metals
  • Explore the concept of relaxation time (τ) and its measurement techniques
  • Study the dynamics of Fermi spheres and their relation to electron behavior in solids
  • Investigate the role of collisions in electron transport and how they affect conductivity
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Physics students, electrical engineers, and researchers in solid-state physics seeking to deepen their understanding of electron dynamics and the Drude model's implications on conductivity.

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As far as I understand: In the Drude model we take the electron to be moving in a random direction after each collision (*), such that the mean velocity is simply the average of -eEt/m, which is just -eEτ/m, where τ is the relaxation time.
But I am very confused about this basic assumption (*), if the electron has a velocity in the direction of the field and suffers collision with another electron, it does not seem likely that the direction of the velocity of the 2 electrons after collision will be completely random.
 
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That was quite helpful. Now I don't suppose you could help me interpreting another
l) states that the equation for the displacement of a Fermi sphere is (all h's are hbars):
h(d/dt + 1/τ)δk = F
Now Newtons law for a completely free electron is:
hdk/dt = F
Why have they put in a δk, and how is the equation to be interpreted? Does it represent the motion of the Fermi sphere in steady state?
 
Probably the variation of k ...

You would get more attention by posting a new question.
 

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