The differential sum rule for the relaxation rate in the cuprates
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abstract
Motivated by recent experiments by Basov {it et al}, we study the differential sum rule for the effective scattering rate $1/ au (omega)$. We show that in a dirty BCS superconductor, the area under $1/ au (omega)$ does not change between the normal and the superconducting states. For magnetically mediated pairing, similar result holds between $T