From a response formula the optical conductivity sigma ( omega ) is derived and evaluated in the Born approximation, with particular emphasis on the effects of phonons. The direct interband part of the conductivity is modified by the Debye-Waller factor which reduces the effect of the periodic potential for increasing temperature. Secondly, a microscopic definition of the relaxation time tau in the phenomenological Drude formula is presented and the frequency dependence of 1/ tau using a Debye model for the phonons is demonstrated.
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K. Sturm (1972) studied this question.
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