We analyze single-electron or exciton transport in long molecules in t
he presence of both static disorder and temporal noise both of which i
nevitably exist in biological systems. The equations for the density m
atrix are derived within an approximation that the temporal noise of t
ransition amplitudes is not correlated. Our model predicts that while
in the short-time limit the transport remains coherent, for sufficient
ly long time the temporal noise causes destruction of the phase cohere
nce, and a crossover from coherent to diffusive transport takes place.
This effect leads to the power-law asymptotic behavior of the transmi
ssion coefficient with the exponent depending on the effective dimensi
onality of the molecule. (C) 1998 Published by Elsevier Science B.V. A
ll rights reserved.