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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.Comment: 59 pages including 8 figures ( REVTEX 3.0 )E-mail:
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