The Dynamic Conductivity in the Relaxation Time Model

  • Wilhelm Brenig


The simple relaxation time ansatz for the collision term allows a complete solution of the linearized Boltzmann equation for arbitrary frequencies and wave numbers. This is what we are going to consider in this chapter. We discuss the response of the density and current density of electrons in isotropic condensed matter to an electric field E. It is assumed to be the total field and we neglect self-consistent exchange fields. The quantity ∂ε/∂p occurring in the drift term (which is only going to be used at the Fermi sphere) will be written as p/m or υ, where m is an effective mass, and υ the Fermi velocity ∣υ∣ = υ f. Then Boltzmann’s equation linearized in the field E in Fourier space takes the form
$$\left( {\omega + \frac{i}{\tau } - \frac{{p \cdot k}}{m}} \right)\delta n\left( {p,k,\omega } \right) - \frac{i}{\tau }\delta {n_l}\left( {p,k,\omega } \right) = - ieE \cdot \frac{{\partial {n_0}}}{{\partial p}} \cdot $$


Dielectric Function Thomas Fermi Linearize Boltzmann Equation Transverse Stiffness Dynamic Conductivity 
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Additional Reading

  1. Drude, P.: Ann. Phys. (Leipzig) 1, 566 (1900)ADSGoogle Scholar
  2. Drude, P.: Ann. Phys. (Leipzig) 3, 369 (1900)ADSGoogle Scholar
  3. Warren, J.L., Ferrell, R.A.: Phys. Rev. 117, 1252 (1960)ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Wilhelm Brenig
    • 1
  1. 1.Physik-DepartmentTechnische Universität MünchenGarchingFed. Rep. of Germany

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