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Examples mobility, conductivity, and diffusion

Consider a homogeneous and isotropic system of classical noninteracting charged particles under an external, position-independent electric field Exit) in the x direction. In this case [Pg.412]

We want to calculate the response to this force as expressed by the average speed of a given particle /, and since in equilibrium (vz)o = 0 we can write [Pg.412]

In focusing on the x component of the response we anticipate that the response in the orthogonal directions vanishes, as can be easily verified using the procedure below. Equation (11.18) takes the form [Pg.413]

In the last equality we have used the fact that the equilibrium velocities of different particles are uncorrelated. For Ex(f) = % = constant Eq. (11.61) gives [Pg.413]

Here and below we have dropped the subscript 0 from the correlation functions. Indeed, to this lowest order we could take the thermal averages using either H or Hq. We have also dropped the subscript I because this result is obviously the same for all identical particles. The equivalent quantum result is [Pg.413]


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