Inversion techniques for optical conductivity data
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Optical data is encoded with information on the microscopic interaction
between charge carriers. For an electron-phonon system, the Eliashberg
equations apply and a Kubo formula can be used to get the infrared
conductivity. The task of extracting the electron-phonon spectral density
$\alpha^2F(\omega)$ from data is rather complicated and, thus, simplified but
approximate expressions for the conductivity have often been used. We test the
accuracy of such simplifications and also discuss the advantages and
disadvantages of various numerical methods needed in the inversion process.
Normal and superconducting state are considered as well as boson exchange
mechanisms which might be applicable to the High-$T_c$ oxides.
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