Sikarin Yoo-Kong, Watchara Liewrian
A model of the electron-transfer process in DNA is investigated by using the Feynman path integral \cite{FHIP,HP,TF,T}. The base-pairs' coordinates are eliminated resulting to the effective action of the system. The trial action is introduced in order to obtain the expectation value of the equation of motion. The electron will be in the equilibrium between lose and gain energy under the presence of an external electric field when the steady-state is reached. Using the result of the steady-state condition, the impedance function of the electron moving along the DNA chain is also studied. Lastly, the effective mass and the mobility of the electron can be directly obtained from the impedance function. For weak coupling, the quadratic dependence of the mobility on temperatures $\mu \sim \mathsf{T}^{-1/2}$ at high temperatures indicates the major role of optical phonon scattering process. At low temperature, the mobility is proportional to the temperature as $\mu \sim \mathsf{T}^{-3/2}$ showing that acoustic phonon scattering dominates the motion of the electron in DNA chain.
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http://arxiv.org/abs/1203.5917
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