异构单文件系统和Rouse链中移动性的普适性和非普适性
Universality and non-universality of mobility in heterogeneous single-file systems and Rouse chains
摘要：
我们分析研究了具有分布摩擦常数的单列系统中示踪粒子的迁移率。我们的系统作为一个原型的非平衡，异构，强相互作用的布朗系统。这种单文件设置的长时间动力学与具有不同珠子的Rouse模型属于相同的通用类。摩擦常数是从密度$\varrho(ξ)$和我们推导出的迁移率分布$P[μ_0(s)]$，其中$μ_0(s)$是拉普拉斯空间迁移率的渐近精确解。如果$\varrho$是轻尾的（一阶矩存在），我们发现一个自平均行为：$P[μ_0(s)]=δ[μ_0(s)-μ(s)]$与$μ(s)\propto s^{1/2}$。当$\varrho(ξ)$是重尾的时，对于大的$\varrho(ξ)\simeq ξ^{-1-α} \ (0<α<1)$，我们得到矩$\langle [μ_s(0)]^n\rangle \propto s^{βn}$，其中$β=1/(1+α)$且没有自平均。模拟结果证实了这一点。
英文摘要：
We study analytically the tracer particle mobility in single-file systems with distributed friction constants. Our system serves as a prototype for non-equilibrium, heterogeneous, strongly interacting Brownian systems. The long time dynamics for such a single-file setup belongs to the same universality class as the Rouse model with dissimilar beads. The friction constants are drawn from a density $\varrho(ξ)$ and we derive an asymptotically exact solution for the mobility distribution $P[μ_0(s)]$, where $μ_0(s)$ is the Laplace-space mobility. If $\varrho$ is light-tailed (first moment exists) we find a self-averaging behaviour: $P[μ_0(s)]=δ[μ_0(s)-μ(s)]$ with $μ(s)\propto s^{1/2}$. When $\varrho(ξ)$ is heavy-tailed, $\varrho(ξ)\simeq ξ^{-1-α} \ (0<α<1)$ for large $ξ$ we obtain moments $\langle [μ_s(0)]^n\rangle \propto s^{βn}$ where $β=1/(1+α)$ and no self-averaging. The results are corroborated by simulations.
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