The interrelation between the condensation energy and the optical sum rules has been investigated. It has been shown that the so called 'partial' sum rule violation is related mainly to a temperature dependence of the relaxation rate rather than to the appearance of superconductivity itself. Moreover, we demonstrate that the experimental data on the temperature dependence of the optical sum rule can be explained rather well by an account of strong electron-phonon interaction.Many recently published works are concerned with the origin of the condensation energy of the superconducting state, a possible violation of so-called 'optical sum rules', and the relation between these phenomena. These papers include both theoretical investigations [1][2][3][4][5][6] of these problems and experimental attempts 7-10 to observe a violation of the optical sum rule. Usually, the possibility of such violation is related to the change of the kinetic en-
The restricted optical sum rule and its dependence on the temperature, a
superconducting gap and the cutoff energy have been investigated. As known this
sum rule depends on the cutoff energy and the relaxation rate even for a
homogeneous electron gas interacting with impurities or phonons. It is shown
here that additional dependence of the spectral weight on a superconducting gap
is very small in this model and this effect disappears totally when the
relaxation rate is equal zero. The model metal with a single band is considered
in details. It is well known that for this model there is the dependence of the
sum rule on the temperature and the energy gap even in the case when the
relaxation is absent. This dependence exists due to the smearing of the
electron distribution function and it is expressed in the terms of Sommerfeld
expansion. Here it is shown that these effects are considerably smaller than
that of related with the relaxation rate if the band width is larger than the
average phonon frequency. It is shown also that the experimental data about the
temperature dependence of the spectral weight for the high- materials can be
successfully explained in the framework approach based on the temperature
dependence of the relaxation rateComment: 13 pages, 7 figures, the talk given on Internatinal coference on
theoretical physics, april 11-16,2005, Mosco
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