A Note on the Analytical Treatment of a Localized Electron-Phonon System Including the Change of Frequency

Abstract

The localized electron-phonon model, which was proposed by Takagahara, Hanamura and Kubo (THK), is extended by including the change of frequency and is treated analytically to obtain the response function and the photon echo signal. Our treatment also gives an analytical expression for the integrand of the transient emission spectrum of the second order optical processes in a localized electron-phonon system which was treated by THK in terms of the eigenvalue problem of the relaxation operator.