Volume 107, Number 1, July 2014
|Number of page(s)||6|
|Published online||09 July 2014|
From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation
1 Dipartimento di Fisica dell'Università di Pisa and INFN - 56127 Pisa, Italy
2 MTA-BME Momentum Statistical Field Theory Research Group - 1111 Budapest, Budafoki út 8, Hungary
3 CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure - 24 rue Lhomond, 75231 Cedex 05, Paris France
Received: 20 May 2014
Accepted: 18 June 2014
We unveil a remarkable connection between the sine-Gordon quantum field theory and the Kardar-Parisi-Zhang (KPZ) growth equation. We find that the non-relativistic limit of the two-point correlation function of the sine-Gordon theory is related to the generating function of the height distribution of the KPZ field with droplet initial conditions, i.e. the directed polymer free energy with two endpoints fixed. As shown recently, the latter can be expressed as a Fredholm determinant which in the large-time separation limit converges to the GUE Tracy-Widom cumulative distribution. Possible applications and extensions are discussed.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.30.Ik – Integrable systems / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
© EPLA, 2014
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