Exact Solution for the Kardar-Parisi-Zhang Equation with Flat Initial Conditions

被引：207

作者：

Calabrese, Pasquale ^{[1
,2
]}

Le Doussal, Pierre ^{[3
]}

机构：

[1] Univ Pisa, Dipartimento Fis, I-56127 Pisa, Italy

[2] Ist Nazl Fis Nucl, I-56127 Pisa, Italy

[3] Ecole Normale Super, CNRS, Phys Theor Lab, F-75231 Paris, France

来源：

PHYSICAL REVIEW LETTERS | 2011年 / 106卷 / 25期

关键词：

PROBABILITY-DISTRIBUTION; POLYNUCLEAR GROWTH; DIRECTED POLYMERS; SCALE-INVARIANCE; FREE-ENERGY; KPZ; DISTRIBUTIONS; BURGERS; SURFACE;

D O I：

10.1103/PhysRevLett.106.250603

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页数：4

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