Table of Contents
ISRN Condensed Matter Physics
Volume 2014, Article ID 719120, 23 pages
Research Article

Projection-Reduction Approach to Optical Conductivities for an Electron-Phonon System and Their Diagram Representation

1Department of Applied Nanoscience, Pusan National University, Miryang 627-706, Republic of Korea
2Department of Physics, Kyungpook National University, Daegu 702-701, Republic of Korea

Received 7 October 2013; Accepted 16 January 2014; Published 7 April 2014

Academic Editors: D. L. Nika and T. Yanagisawa

Copyright © 2014 Nam Lyong Kang and Sang Don Choi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Utilizing state-dependent projection operators and the Kang-Choi reduction identities, we derive the linear, first, and second-order nonlinear optical conductivities for an electron system interacting with phonons. The lineshape functions included in the conductivity tensors satisfy “the population criterion” saying that the Fermi distribution functions for electrons and Planck distribution functions for phonons should be combined in multiplicative forms. The results also contain energy denominator factors enforcing the energy conservation as well as interaction factors describing electron-phonon interaction properly. Therefore, the phonon absorption and emission processes as well as photon absorption and emission processes in all electron transition processes can be presented in an organized manner and the results can be represented in diagrams that can model the quantum dynamics of electrons in a solid.