Double path-integral method for obtaining the mobility of the   one-dimensional charge transport in molecular chain
  We report on a theoretical investigation concerning the polaronic effect on the transport properties of a charge carrier in the one-dimensional molecular chain. Our technique is based on the Feynman's path integral approach. Analytical expressions for the frequency-dependent mobility and effective mass of the carrier are obtained as functions of electron-phonon coupling. The result exhibits the crossover from a nearly free particle to a heavily trapped particle. We find that the mobility depends on temperature and decreases exponentially with increasing temperature at low temperature. It exhibits large-polaronic-like behaviour in the case of weak electron-phonon coupling. These results agree with the phase transition \cite{Mish} of transport phenomena related to polaron motion in the molecular chain. 
Sikarin Yoo-Kong and Watchara Liewrian
cond-mat.mes-hall cond-mat.soft math-ph math.MP