Probability distribution of the free energy of a directed polymer in a random medium.
Probability distribution of the free energy of a directed polymer in a random medium.
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随机介质中定向聚合物自由能的概率分布。
DOI：
10.1103/physreve.61.6789
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
B. Derrida
中科院分区：
文献类型：
--
作者：
E. Brunet;B. Derrida
我们精确地计算了圆柱体几何形状的定向聚合物在无规介质中自由能的第一累积量。利用配分函数的n阶矩是由长度为L的环上n个相互作用粒子的量子问题的基态能量给出的这一事实，我们写出一个积分方程，允许将这些矩扩展为无序γ的强度的幂或n的幂。对于n小和n约（Lgamma）（-1/2），矩采取标度形式，其允许我们描述定向聚合物的每单位长度的自由能的1/L级的所有波动。这些涨落的分布与最近在不对称排斥过程中发现的涨落的分布相同，表明它是1+1维Kardar-Parisi-Zhang方程描述的所有系统的特征。
We calculate exactly the first cumulants of the free energy of a directed polymer in a random medium for the geometry of a cylinder. By using the fact that the nth moment of the partition function is given by the ground-state energy of a quantum problem of n interacting particles on a ring of length L, we write an integral equation allowing to expand these moments in powers of the strength of the disorder gamma or in powers of n. For n small and n approximately (Lgamma)(-1/2), the moments take a scaling form which allows us to describe all the fluctuations of order 1/L of the free energy per unit length of the directed polymer. The distribution of these fluctuations is the same as the one found recently in the asymmetric exclusion process, indicating that it is characteristic of all the systems described by the Kardar-Parisi-Zhang equation in 1+1 dimensions.