Dipartimento di Fisica dell'Università di Pisa and INFN, 56127 Pisa, Italy.
Phys Rev Lett. 2011 Jun 24;106(25):250603. doi: 10.1103/PhysRevLett.106.250603.
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.
我们提供了在一维平面初始条件下任意时间 t 的连续 Kardar-Parisi-Zhang（KPZ）增长方程高度分布的首次精确计算。我们使用映射到一端固定、一端自由的有向聚合物，并对复制吸引玻色子模型进行 Bethe 近似。我们得到了有向聚合物配分函数矩的生成函数，它是 Fredholm Pfaffian。我们的公式在所有时间都有效，显示出自由能（即 KPZ 高度）分布在大时间时收敛到高斯正交系综 Tracy-Widom 分布。
