# Anomalous Fluctuations of

# Directed Polymers in Random Media

Terence Hwa and Daniel S. Fisher

## Abstract

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.

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