Dynamics of directed polymers with cutting interactions

An equation for the time evolution of the density of directed polymers is derived in the limit of a high rate of cutting. The equilibrium solution is found to be equivalent to that obtained from the transfer-matrix approach for a single directed polymer. For potentials that depend only on the transverse coordinates, the logarithm of the mobility is found to behave as ∼(-U^1/2), or barrier height U. Application to the motion of flux lines in superconductors is briefly discussed.