Two-point generating function of the free energy for a directed polymer in a random medium

Sylvain Prolhac, Herbert Spohn

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Abstract

We consider a (1 + 1)-dimensional directed continuum polymer in a Gaussian delta-correlated spacetime random potential. For this model the moments (= replica) of the partition function, Z(x,t), can be expressed in terms of the attractive δ-Bose gas on the line. Based on a recent study of the structure of the eigenfunctions, we compute the generating function for Z(x 1,t), Z(x2,t) under a particular decoupling assumption and thereby extend recent results on the one-point generating function of the free energy to two points. It is established that in the long-time limit the fluctuations of the free energy are governed by the two-point distribution of the Airy process, which further supports that the longtime behavior of the KPZ equation is the same as derived previously for lattice growth models.

Original languageEnglish
Article numberP01031
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2011
Issue number1
DOIs
StatePublished - Jan 2011

Keywords

  • Disordered systems (theory)
  • Quantum integrability (Bethe ansatz)

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