某些非平衡系统中有序态与无序态的交叉
Crossover Between Organized and Disorganized States In Some Non-Equilibrium Systems
摘要：
本文用数值方法研究了三种非平衡系统：Poisson/CoalesceRandomWalk（PCRW）、一维自旋系统和准一维格子气的有序态和无序态之间的交叉。在所有情况下，我们描述这种交叉粒子/域边界之间的平均间距$< S(t) >$和间距分布函数$p^{(n)}(s)$。交叉的性质对于所有系统是不相同的，然而，我们发现对于所有系统，最近邻分布$p^{(0)}(s)$很好地拟合Berry-Robnik模型。在有组织状态和无组织状态之间的交叉中，能级排斥的破坏存在于所有系统中。此外，我们发现，在气体和自旋系统的域之间的相关性并不强，可以忽略不计，在第一近似，但对于PCRW粒子之间的相关性必须考虑。为了用$n>1$找到$p^{(n)}(s)$，我们在Berry-Robnik模型的基础上提出了两种不同的分析模型。我们的模型为这些系统在交叉时的统计行为提供了一个很好的近似，并允许我们量化系统的有序/无序程度。
英文摘要：
We study numerically the crossover between organized and disorganized states of three non-equilibrium systems: the Poisson/coalesce random walk (PCRW), a one-dimensional spin system and a quasi one-dimensional lattice gas. In all cases, we describe this crossover in terms of the average spacing between particles/domain borders $< S(t) >$ and the spacing distribution functions $p^{(n)}(s)$. The nature of the crossover is not the same for all systems, however, we found that for all systems the nearest neighbor distribution $p^{(0)}(s)$ is well fitted by the Berry-Robnik model. The destruction of the level repulsion in the crossover between organized an disorganized states is present in all systems. Additionally, we found that the correlations between domains in the gas and spin systems are not strong and can be neglected in a first approximation but for the PCRW the correlations between particles must be taken into account. To find $p^{(n)}(s)$ with $n>1$, we propose two different analytical models based on the Berry-Robnik model. Our models give us a good approximation for the statistical behavior of these systems in their crossover and allow us to quantify the degree of order/disorder of the system.
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