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We propose a possible way to simulate a hump structure in the opticalscattering rate. The optical scattering rate of correlated charge carriers canbe defined within an extended Drude model formalism. When some electron andhole doped copper oxide systems are in the spin density or charge density wavephases they show hump structures in their optical scattering rates. The humpstructures have not yet been simulated and understood clearly. We are able tosimulate the hump structure by using a peak followed by a dip feature in thenormalized density of states within a generalized Allen formalism. We observethat reversing the order of the dip and peak gives completely differentfeatures in the optical scattering rate; a peak-dip (dip peak) results in ahump (a valley) in the scattering rate. We also obtain the real part of theoptical conductivity and reflectance spectra from the simulated opticalscattering rate and compare them with published experimental spectra. Fromthese comparisons we conclude that the peak-dip order can give the humpstructure, which is observed experimentally in copper oxide systems. Finally wefit two published optical spectra with our new model and discuss our resultsand the possible origin of the dip or peak features in the normalized densityof states.

Simulation of a hump structure in the optical scattering rate within a generalized Allen formalism and its application to copper oxide systems