标题： 分数阶扩散方程对开放异常热传导装置的描述 显示英文标题

标题： Fractional diffusion equation description of an open anomalous heat conduction set-up

摘要： 我们提供了一个随机分数阶扩散方程，用于描述通过具有随机动量交换并连接到朗之万型热浴的有限一维谐振子链中的能量传输。 通过建立相关分数算子的明确有限域表示，我们表明该方程可以正确再现平衡性质，如格林-库博公式，以及非平衡性质，如稳态温度和电流。 此外，该方程提供了温度分布的精确时间演化。 结合对扩散系统和数值模拟的洞察，我们提出一个猜想，即稳态中的长程相关性由分数算子的逆给出。 我们还指出了分数算子谱的一些有趣性质。 我们所有的分析结果都得到了微观系统的广泛数值模拟的补充。 显示英文摘要

摘要： We provide a stochastic fractional diffusion equation description of energy transport through a finite one-dimensional chain of harmonic oscillators with stochastic momentum exchange and connected to Langevian type heat baths at the boundaries. By establishing an unambiguous finite domain representation of the associated fractional operator, we show that this equation can correctly reproduce equilibrium properties like Green-Kubo formula as well as non-equilibrium properties like the steady state temperature and current. In addition, this equation provides the exact time evolution of the temperature profile. Taking insights from the diffusive system and from numerical simulations, we pose a conjecture that these long-range correlations in the steady state are given by the inverse of the fractional operator. We also point out some interesting properties of the spectrum of the fractional operator. All our analytical results are supplemented with extensive numerical simulations of the microscopic system.