Pair-factorized steady states on arbitrary graphs
Pair-factorized steady states on arbitrary graphs
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DOI：
10.1088/1751-8113/42/31/315003
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发表时间：
2009-04
期刊：
影响因子：
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通讯作者：
B. Wacław;J. Sopik;W. Janke;H. Meyer-Ortmanns
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文献类型：
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作者：
B. Wacław;J. Sopik;W. Janke;H. Meyer-Ortmanns
随机质量输运模型通常通过指定粒子在给定晶格的位置之间的跳跃速率来描述，目标是预测稳态的存在和性质。在这里，我们问相反的问题：给定一个固定状态，分解的链接（对网站）的任意连接图，什么是可能的跳跃率收敛到这个状态？我们定义了一类动力系统，导致相同的稳定状态，并保证电流守恒，但可能不同的感应电流强度。对于二维各向异性跳跃的特殊情况，我们讨论了相结构的一些方面。我们还展示了这种情况下可以追溯到一个有效的零范围的过程中的一个维度，这是可解的一大类跳跃函数。
Stochastic mass transport models are usually described by specifying hopping rates of particles between sites of a given lattice, and the goal is to predict the existence and properties of the steady state. Here we ask the reverse question: given a stationary state that factorizes over links (pairs of sites) of an arbitrary connected graph, what are possible hopping rates that converge to this state? We define a class of dynamical systems which lead to the same steady state and guarantee current conservation but may differ by the induced current strength. For the special case of anisotropic hopping in two dimensions, we discuss some aspects of the phase structure. We also show how this case can be traced back to an effective zero-range process in one dimension which is solvable for a large class of hopping functions.