DIRECTED POLYMERS IN THE PRESENCE OF COLUMNAR DISORDER

We consider directed polymers in a random landscape that is completely correlated in the time direction. This problem is closely related to diffusion-reproduction processes and undirected Gaussian polymers in a disordered environment. In contrast to the case of uncorrelated disor der, we find the behavior to be very different at zero temperature, wh ere the scaling exponents depend on the details of the random energy d istribution, and at finite temperature, where the transverse wandering is subballistic, x is similar to t/(log t)gamma with gamma = 1 + 2/d for bounded distributions in d + 1 dimensions. Numerically, these stro ng logarithmic corrections give rise to apparently nontrivial effectiv e exponents. Our analytic results axe based on appropriate Flory expre ssions for the (free) energy at T = 0 and T > 0. Some universal statis tical properties of the evolutionary hopping of the optimal path axe a lso derived.