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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.