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Probability distribution of the free energy of a directed polymer in a random medium.

Authors
  • Brunet, E
  • Derrida, B
Type
Published Article
Journal
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
Publication Date
Jun 01, 2000
Volume
61
Issue
6 Pt B
Pages
6789–6801
Identifiers
PMID: 11088374
Source
Medline
License
Unknown

Abstract

We calculate exactly the first cumulants of the free energy of a directed polymer in a random medium for the geometry of a cylinder. By using the fact that the nth moment <Z(n)> of the partition function is given by the ground-state energy of a quantum problem of n interacting particles on a ring of length L, we write an integral equation allowing to expand these moments in powers of the strength of the disorder gamma or in powers of n. For n small and n approximately (Lgamma)(-1/2), the moments <Z(n)> take a scaling form which allows us to describe all the fluctuations of order 1/L of the free energy per unit length of the directed polymer. The distribution of these fluctuations is the same as the one found recently in the asymmetric exclusion process, indicating that it is characteristic of all the systems described by the Kardar-Parisi-Zhang equation in 1+1 dimensions.

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