无序中的伸展指数松弛与ac普适性 电介质

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摘要翻译：
本文研究了无序介质中的介电弛豫性质与交流导电的关系。讨论分为经典线性响应理论和自洽动力学模型。研究的关键问题是介质弛豫的伸展指数特性、功率谱密度的幂律性以及交流传导系数对频率的反常依赖性。我们提出了一个自洽的介电弛豫模型，其中弛豫用一个拉伸的指数衰减函数来描述。在数学上，我们的研究涉及到分数阶微积分的扩展区域，从ac普适性出发，对分数阶松弛方程和分数阶扩散方程进行了系统的推导。
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英文标题：
《Stretched exponential relaxation and ac universality in disordered
  dielectrics》
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作者：
Alexander V. Milovanov (Department of Physics and Technology,
  University of Tromso, Tromso, Norway), Jens Juul Rasmussen (Optics and Plasma
  Research Department, Riso National Laboratory, Technical University of
  Denmark, Roskilde, Denmark), Kristoffer Rypdal (Department of Physics and
  Technology, University of Tromso, Tromso, Norway)
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--

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英文摘要：
  This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a self-consistent dynamical modeling. The key issues are, stretched exponential character of dielectric relaxation, power-law power spectral density, and anomalous dependence of ac conduction coefficient on frequency. We propose a self-consistent model of dielectric relaxation, in which the relaxations are described by a stretched exponential decay function. Mathematically, our study refers to the expanding area of fractional calculus and we propose a systematic derivation of the fractional relaxation and fractional diffusion equations from the property of ac universality.
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PDF链接：
https://arxiv.org/pdf/705.4417

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关键词：localization Mathematical Exponential Alternating mathematica 指数 fractional 方程 线性 研究