Dynamical scaling exponents for polymer translocation through a nanopore

We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to N=800 in some cases. We focus on the scaling of the average PT time tau similar to N-alpha and the mean-square change of the PT coordinate, < s(2)(t)>similar to t(beta). We find alpha=1+2 nu and beta=2/alpha for unbiased PT in two dimensions (2D) and three dimensions (3D). The relation alpha beta=2 holds for driven PT in 2D, with a crossover from alpha approximate to 2 nu for short chains to alpha approximate to 1+nu for long chains. This crossover is, however, absent in 3D where alpha=1.42 +/- 0.01 and alpha beta approximate to 2.2 for N approximate to 40-800.