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Exact solution for the Kardar-Parisi-Zhang equation with flat initial conditions.

Authors :
Calabrese P
Le Doussal P
Source :
Physical review letters [Phys Rev Lett] 2011 Jun 24; Vol. 106 (25), pp. 250603. Date of Electronic Publication: 2011 Jun 24.
Publication Year :
2011

Abstract

We provide the first exact calculation of the height distribution at arbitrary time t of the continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial conditions. We use the mapping onto a directed polymer with one end fixed, one free, and the Bethe ansatz for the replicated attractive boson model. We obtain the generating function of the moments of the directed polymer partition sum as a Fredholm Pfaffian. Our formula, valid for all times, exhibits convergence of the free energy (i.e., KPZ height) distribution to the Gaussian orthogonal ensemble Tracy-Widom distribution at large time.

Details

Language :
English
ISSN :
1079-7114
Volume :
106
Issue :
25
Database :
MEDLINE
Journal :
Physical review letters
Publication Type :
Academic Journal
Accession number :
21770622
Full Text :
https://doi.org/10.1103/PhysRevLett.106.250603