Exact stationary state for an asymmetric exclusion process with fully parallel dynamics.
Exact stationary state for an asymmetric exclusion process with fully parallel dynamics.
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DOI：
10.1103/physreve.59.4899
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发表时间：
1998-12
期刊：
影响因子：
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通讯作者：
J. Gier;B. Nienhuis
中科院分区：
文献类型：
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作者：
J. Gier;B. Nienhuis
利用矩阵积分析方法，得到了具有完全并行动力学的不对称不相容过程的精确定态。通过对矩阵维数的物理解释，给出了确定性情况下的简单推导。我们通过消去机制证明了平稳性，并利用矩阵代数的显式表示，很容易找到一般概率情况下相关函数的闭表达式。利用前面的结果得到的渐近表达式，使我们能够推导出确切的相图。
The exact stationary state of an asymmetric exclusion process with fully parallel dynamics is obtained using the matrix product ansatz. We give a simple derivation for the deterministic case by a physical interpretation of the dimension of the matrices. We prove the stationarity via a cancellation mechanism, and by making use of an explicit representation of the matrix algebra we easily find closed expressions for the correlation functions in the general probabilistic case. Asymptotic expressions, obtained by making use of earlier results, allow us to derive the exact phase diagram.