Abstract
A new diagram method for the line shape function in the optical conductivity formula is introduced and the result obtained applying the method to an electron-phonon system is compared with that derived using the projection-reduction method. The result satisfies the population criterion, which states that the distribution functions for electrons and phonons should be combined in multiplicative forms and gives physical intuition to quantum dynamics of electrons in a solid. This method can be called the “KC diagram” method because it originates from the proper application of the Kang-Choi reduction identity and a state-dependent projection operator.
Highlights
Studies of the optical transitions in electron systems are powerful for examining the electronic properties of solids because the absorption line shapes are quite sensitive to the type of scattering mechanism affecting the transport of electrons and to the interaction of electrons with intense laser light
We introduced a new diagram method for the line shape function in the optical conductivity tensor for an electron-phonon system
We showed that the same result as that derived using the PR method could be obtained more and in a physically acceptable manner using the present diagram method
Summary
Studies of the optical transitions in electron systems are powerful for examining the electronic properties of solids because the absorption line shapes are quite sensitive to the type of scattering mechanism affecting the transport of electrons and to the interaction of electrons with intense laser light. A perturbation-based study is a general method for gaining knowledge on the dynamics of a system. This consists of dividing the Hamiltonian into an exactly soluble part and nontrivial perturbative part, the effects of which are studied in perturbative order. The Feynman diagram is the most popular method for representing the terms in perturbative expressions. This diagrammatic method can be used directly for reasoning and problem solving as well as for representing the perturbative expressions by drawings. The recognizable topology of the diagrams makes the diagrammatic method a powerful tool for constructing approximation schemes. The diagrammatic representation can be a suggestive tool providing physical intuition vital to quantum dynamics by increasing the diagrams to a representation for possible alternative physical processes
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