Midpoint Distribution of Directed Polymers in the Stationary Regime: Exact Result Through Linear Response
Midpoint Distribution of Directed Polymers in the Stationary Regime: Exact Result Through Linear Response
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DOI：
10.1007/s10955-017-1839-2
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发表时间：
2017-04
影响因子：
1.6
通讯作者：
C. Maes;Thimothée Thiery
中科院分区：
文献类型：
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作者：
C. Maes;Thimothée Thiery
我们得到一个精确的结果的中点概率分布函数（PDF）的固定连续定向聚合物，平均超过无序。它是通过将pdf与随机Burgers场对某些扰动的线性响应相关联而获得的。从随机Burgers方程的对称性出发，我们导出了一个涨落耗散关系，使得概率密度函数由Burgers场的平稳两个时空点的相关函数给出.后者的解析表达式由Imamura和Sasamoto（J Stat Phys 150：908-939，2013）获得，从而使我们的结果明确。在大长度限制下，这意味着pdf只不过是Prähofer和Spohn引入的标度函数（J Stat Phys 115（1）：255-279，2004）。使用KPZ-普适性范式，我们发现，这个函数因此也可以被解释为的位置的pdf的最大值的艾里过程减去抛物线和双边布朗运动。我们提供了一个直接的数值测试的结果，通过模拟的对数伽马聚合物。
We obtain an exact result for the midpoint probability distribution function (pdf) of the stationary continuum directed polymer, when averaged over the disorder. It is obtained by relating that pdf to the linear response of the stochastic Burgers field to some perturbation. From the symmetries of the stochastic Burgers equation we derive a fluctuation–dissipation relation so that the pdf gets given by the stationary two space-time points correlation function of the Burgers field. An analytical expression for the latter was obtained by Imamura and Sasamoto (J Stat Phys 150:908–939, 2013), thereby rendering our result explicit. In the large length limit that implies that the pdf is nothing but the scaling functionintroduced by Prähofer and Spohn (J Stat Phys 115(1):255–279, 2004). Using the KPZ-universality paradigm, we find that this function can therefore also be interpreted as the pdf of the positionyof the maximum of the Airy process minus a parabola and a two-sided Brownian motion. We provide a direct numerical test of the result through simulations of the Log-Gamma polymer.