A Compendium of Solid State Theory by Ladislaus Alexander Bányai

Author:Ladislaus Alexander Bányai
Language: eng
Format: epub, pdf
ISBN: 9783030373597
Publisher: Springer International Publishing

In the same way one may get also

However, as it may be seen easily that

and

Therefore, from the above equations it follows:

while

From the conditions , together with the above relations we get immediately

The first of these relations is just the well-known Einstein relation between the electrical conductivity and the diffusion coefficient.

Now we may rewrite the general expressions of the average currents as

To derive the expressions of the remaining coefficients and one has to develop a little bit of fantasy. The Luttinger approach follows the idea of the Einstein relation, by introducing the interaction with a fictitious gravitational field ψ(x) interacting with the Hamiltonian density ρ E(x) as

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