Anomalous fluctuations of directed polymers in random media.

A systematic analysis of large-scale fluctuations in the low-temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ground states.'' The probability distribution of their sizes is found to have a power-law tail. The rare regions in the tail dominate much of the physics. The analysis presented here takes advantage of the mapping to the noisy Burgers' equation. It complements a phenomenological description of glassy phases based on a scaling picture of droplet excitations and a recent variational approach with broken replica symmetry.'' It is argued that the power-law distribution of large thermally active excitations is a consequence of the continuous statistical tilt'' symmetry of the directed polymer, the breaking of which gives rise to the large active excitations in a manner analogous to the appearance of Goldstone modes in pure systems with a broken continuous symmetry.