Gueudré Thomas, Le Doussal Pierre, Rosso Alberto, Henry Adrien, Calabrese Pasquale
CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):041151. doi: 10.1103/PhysRevE.86.041151. Epub 2012 Oct 31.
The short-time behavior of the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) growth equation with a flat initial condition is obtained from the exact expressions for the moments of the partition function of a directed polymer with one end point free and the other fixed. From these expressions, the short-time expansions of the lowest cumulants of the KPZ height field are exactly derived. The results for these two classes of cumulants are checked in high-precision lattice numerical simulations. The short-time limit considered here is relevant for the study of the interface growth in the large-diffusivity or weak-noise limit and describes the universal crossover between the Edwards-Wilkinson and the KPZ universality classes for an initially flat interface.
具有平坦初始条件的(1+1)维 Kardar-Parisi-Zhang（KPZ）增长方程的短时行为，是通过一端自由而另一端固定的定向聚合物配分函数矩的精确表达式得到的。从这些表达式中，精确推导了 KPZ 高度场最低累积量的短时展开式。这两类累积量的结果在高精度晶格数值模拟中得到了检验。这里考虑的短时极限与大扩散率或弱噪声极限下的界面生长研究相关，并且描述了初始平坦界面在 Edwards-Wilkinson 和 KPZ 普适类之间的普适交叉。
