LONG-TIME TAILS IN STATIONARY RANDOM-MEDIA .1. THEORY
LONG-TIME TAILS IN STATIONARY RANDOM-MEDIA .1. THEORY
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DOI：
10.1007/bf01018555
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发表时间：
1984-01-01
影响因子：
1.6
通讯作者：
VANBEIJEREN, H
中科院分区：
文献类型：
--
作者：
ERNST, MH;MACHTA, J;VANBEIJEREN, H
用唯象模式耦合理论研究了运动粒子在静止无序介质中的扩散。无序的存在导致广义扩散方程，记忆内核具有幂律长时间尾巴。速度自相关函数的衰减类似于t−（d/2+1），而与超伯内特系数相关的时间相关函数的衰减类似于ket −d/2。该理论适用于各种各样的动力学和随机系统，包括洛伦兹气体和跳跃模型。我们找到了新的，一般的表达式的系数的长时间的尾巴，同意与以前的结果完全可解的跳跃模型和低密度的结果得到的洛伦兹气体。最后，我们提到，如果运动的粒子是带电的，那么长时间的尾巴意味着有一个ωd/2的频率依赖电导率的低频部分的贡献。
Diffusion of moving particles in stationary disordered media is studied using a phenomenological mode-coupling theory. The presence of disorder leads to a generalized diffusion equation, with memory kernels having power law long time tails. The velocity autocorrelation function is found to decay like t−(d/2+1), while the time correlation function associated with the super-Burnett coefficient decays liket−d/2for long times. The theory is applicable to a wide variety of dynamical and stochastic systems including the Lorentz gas and hopping models. We find new, general expressions for the coefficients of the long time tails which agree with previous results for exactly solvable hopping models and with the low-density results obtained for the Lorentz gas. Finally we mention that if the moving particles are charged, then the long time tails imply that there is an ωd/2contribution to the low-frequency part of the frequency-dependent electrical conductivity.