The KPZ equation with flat initial condition and the directed polymer with one free end
The KPZ equation with flat initial condition and the directed polymer with one free end
复制标题
具有平坦初始条件的 KPZ 方程和具有一个自由端的定向聚合物
DOI：
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复制
发表时间：
2012
期刊：
影响因子：
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通讯作者：
P. Calabrese
中科院分区：
文献类型：
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作者：
P. Le Doussal;P. Calabrese
研究了连续体极限中1+1维随机势中长度为t的定向聚合物，其中一端是固定的，另一端是自由的。这映射到时间t的Kardar-Parisi-Zhang增长方程上，初始条件是平的。我们使用Bethe ansatz解来解决复制问题，这是一个吸引人的玻色子模型。这个问题比以前的固定端点问题的解更困难，因为它需要Bethe特征函数上的空间积分的正则化。我们要么使用大的固定系统长度，要么使用小的有限斜率Kpz初始条件(楔形)。后者允许人们适当地考虑非平凡的贡献，在前者中表现为变形的弦。通过在适当的极限下考虑半空间模型，我们得到了有向聚合物配分函数的所有正整数矩的母函数的表达式。我们得到了DP分拆和的矩的母函数作为FredholmPfaffian。在很大的时间内，这种在所有时间t都有效的FredholmPfaffian表现出自由能(即KPZ高度)分布到GOE Tracy-Widom分布的收敛。
We study the directed polymer (DP) of length t in a random potential in dimension 1 + 1 in the continuum limit, with one end fixed and one end free. This maps onto the Kardar–Parisi–Zhang growth equation in time t, with flat initial conditions. We use the Bethe ansatz solution for the replicated problem, which is an attractive bosonic model. The problem is more difficult than the previous solution of the fixed endpoint problem as it requires regularization of the spatial integrals over the Bethe eigenfunctions. We use either a large fixed system length or small finite slope KPZ initial conditions (wedge). The latter allows one to take properly into account non-trivial contributions, which appear as deformed strings in the former. By considering a half-space model in a proper limit we obtain an expression for the generating function of all positive integer moments of the directed polymer partition function. We obtain the generating function of the moments of the DP partition sum as a Fredholm Pfaffian. At large time, this Fredholm Pfaffian, valid for all time t, exhibits convergence of the free energy (i.e. KPZ height) distribution to the GOE Tracy–Widom distribution.
影响因子：
3
作者：
Borodin, Alexei;Corwin, Ivan;Ferrari, Patrik
通讯作者：
Ferrari, Patrik
影响因子：
3.1
作者：
Ivan Corwin;A. Hammond
通讯作者：
Ivan Corwin;A. Hammond