TY - JOUR

T1 - Two-point generating function of the free energy for a directed polymer in a random medium

AU - Prolhac, Sylvain

AU - Spohn, Herbert

PY - 2011/1

Y1 - 2011/1

N2 - 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.

AB - 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.

KW - Disordered systems (theory)

KW - Quantum integrability (Bethe ansatz)

UR - http://www.scopus.com/inward/record.url?scp=79751501755&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2011/01/P01031

DO - 10.1088/1742-5468/2011/01/P01031

M3 - Article

AN - SCOPUS:79751501755

SN - 1742-5468

VL - 2011

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 1

M1 - P01031

ER -