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arXiv 1012.0423cond-mat.stat-mech
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开放超扩散系统的密度分布

Density Profiles in Open Superdiffusive Systems

Stefano Lepri, Antonio Politi

摘要:

我们数值求解了一个有限一维区域上的Levy随机游动的离散化模型,该模型中存在源和反射系数$r$。在域边界处,稳态密度分布是非解析的。引入弯月面指数$μ$来表征这种奇异行为,唯一地标识整个轮廓。数值数据表明,$μ=α/2 + r(α/2-1)$,其中$α$是步长分布的Levy指数。作为一个应用程序,我们表明,该模型再现了显示异常热传导的振荡器链获得的温度分布。值得注意的是,链中的自由边界条件的情况下,对应于一个Levy行走与负反射系数。

英文摘要:

We numerically solve a discretized model of Levy random walks on a finite one-dimensional domain in the presence of sources and with a reflection coefficient $r$. At the domain boundaries, the steady-state density profile is non-analytic. The meniscus exponent $μ$, introduced to characterize this singular behavior, uniquely identifies the whole profile. Numerical data suggest that $μ=α/2 + r(α/2-1)$, where $α$ is the Levy exponent of the step-length distribution. As an application, we show that this model reproduces the temperature profiles obtained for a chain of oscillators displaying anomalous heat conduction. Remarkably, the case of free-boundary conditions in the chain correspond to a Levy walk with negative reflection coefficient.

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