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摘要翻译：
一维Burgers方程的动力学标度特性随着附加守恒自由度的加入而改变。我们用一维驱动的守恒质量和动量的格子气模型来研究这一点。最基本的是Arndt-Heinzel-Rittenberg(AHR)过程，它通常表现为两物种扩散过程，相反电荷的粒子以不同的通过概率向相反的方向跳跃。从流体力学角度看，这可以看作是两个耦合的Burgers方程，正负动量量子个数各自守恒。我们从两点相关函数的时间演化确定了AHR过程的动力学标度维数，并通过数值计算发现动力学临界指数与简单Kardar-Parisi-Zhang(KPZ)型标度一致。我们确定这是对定态中涨落的完美筛选的结果。在我们的模拟中，两点关联以指数方式衰减，对于准粒子来说，涨落在粗粒度长度尺度上完全相互屏蔽。我们用稳态的解析矩阵乘积结构严格地证明了这种筛选。证明了拓扑不变量的存在性。该过程仍在KPZ普遍性类中，但仅在因式分解的意义上，如$({KPZ}）^2$。由于完全屏蔽，两个Burgers方程在大尺度上解耦。
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英文标题：
《Dynamic Screening in a Two-Species Asymmetric Exclusion Process》
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作者：
Kyung Hyuk Kim and Marcel den Nijs
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
The dynamic scaling properties of the one dimensional Burgers equation are expected to change with the inclusion of additional conserved degrees of freedom. We study this by means of 1-D driven lattice gas models that conserve both mass and momentum. The most elementary version of this is the Arndt-Heinzel-Rittenberg (AHR) process, which is usually presented as a two species diffusion process, with particles of opposite charge hopping in opposite directions and with a variable passing probability. From the hydrodynamics perspective this can be viewed as two coupled Burgers equations, with the number of positive and negative momentum quanta individually conserved. We determine the dynamic scaling dimension of the AHR process from the time evolution of the two-point correlation functions, and find numerically that the dynamic critical exponent is consistent with simple Kardar-Parisi-Zhang (KPZ) type scaling. We establish that this is the result of perfect screening of fluctuations in the stationary state. The two-point correlations decay exponentially in our simulations and in such a manner that in terms of quasi-particles, fluctuations fully screen each other at coarse grained length scales. We prove this screening rigorously using the analytic matrix product structure of the stationary state. The proof suggests the existence of a topological invariant. The process remains in the KPZ universality class but only in the sense of a factorization, as $({KPZ})^2$. The two Burgers equations decouple at large length scales due to the perfect screening.
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PDF链接：
https://arxiv.org/pdf/705.1377
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