Barrier crossing in one and three dimensions by a long chain

Abstract

We consider the Kramers problem for a long chain polymer trapped in abiased double-well potential. Initially the polymer is in the less stable welland it can escape from this well to the other well by the motion of itsN beads across the barrier to attain the configuration having lower free energy. In onedimension we simulate the crossing and show that the results are in agreement with thekink mechanism suggested earlier. In three dimensions, it has not been possible to get ananalytical ‘kink solution’ for an arbitrary potential; however, one can assume the form ofthe solution of the nonlinear equation as a kink solution and then find a double-wellpotential in three dimensions. To verify the kink mechanism, simulations of the dynamics ofa discrete Rouse polymer model in a double well in three dimensions are carried out.We find that the time of crossing is proportional to the chain length, which isin agreement with the results for the kink mechanism. The shape of the kinksolution is also in agreement with the analytical solution in both one and threedimensions.