Universal Large-Deviation Function of the Kardar–Parisi–Zhang Equation in One Dimension
Universal Large-Deviation Function of the Kardar–Parisi–Zhang Equation in One Dimension
复制标题
一维Kardar-Parisi-Zhang方程的通用大偏差函数
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
C. Appert
中科院分区：
文献类型：
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作者：
Bernard Derrida;C. Appert
利用Bethe近似计算了环上非对称简单排斥过程（ASEP）中粒子位移的大偏差函数。当环的尺寸很大时，这个大偏差函数的中心部分采取与粒子密度无关的标度形式。我们认为，这个标度函数发现的ASEP是普遍的，应该是所有系统的特征所描述的Kardar-Parisi-Zhang方程在1+1维。对两个简单增长模型的模拟与这一猜想基本一致。
Using the Bethe ansatz, we calculate the whole large-deviation function of the displacement of particles in the asymmetric simple exclusion process (ASEP) on a ring. When the size of the ring is large, the central part of this large deviation function takes a scaling form independent of the density of particles. We suggest that this scaling function found for the ASEP is universal and should be characteristic of all the systems described by the Kardar–Parisi–Zhang equation in 1+1 dimension. Simulations done on two simple growth models are in reasonable agreement with this conjecture.