Effect of temporal noise on the single-electron transport in long molecules

We analyze single-electron or exciton transport in long molecules in the presence of both static disorder and temporal noise both of which inevitably exist in biological systems. The equations for the density matrix are derived within an approximation that the temporal noise of transition amplitudes is not correlated. Our model predicts that while in the short-time limit the transport remains coherent, for sufficiently long time the temporal noise causes destruction of the phase coherence, and a crossover from coherent to diffusive transport takes place. This effect leads to the power-law asymptotic behavior of the transmission coefficient with the exponent depending on the effective dimensionality of the molecule.