Sum rule for optical scattering rates
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An important quantity in electronic systems is the quasiparticle scattering
rate (QPSR). A related optical scattering rate (OSR) is routinely extracted
from optical data, and, while it is not the same as the QPSR, it nevertheless
displays many of the same features. We consider a sum rule which applies to the
area under a closely related quantity, almost equal to the OSR in the low
energy region. We focus on the readjustment caused by, for example, a
quasiparticle density of states change due to the superconducting transition.
Unfortunately, no general statement about mechanism can be made solely on the
energy scale in which the spectral weight readjustment on the OSR occurs.