Anomalous diffusion in aperiodic environments
Anomalous diffusion in aperiodic environments
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非周期环境中的反常扩散
DOI：
10.1103/physreve.59.1465
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发表时间：
1998
影响因子：
2.4
通讯作者：
Forschungszentrum Juelich
中科院分区：
文献类型：
--
作者：
F. Iglói;L. Turban;H. I. O. T. Physics;Budapešť;U. Szeged;H. P. University;Nancy;Hlrz;Forschungszentrum Juelich
研究了一维非均匀环境中经典粒子的布朗运动，其中跃迁概率服从准周期或非周期分布。利用非均匀耦合横场伊辛模型的精确对应，我们得到了随机行走问题的许多解析结果。在不存在全局偏差的情况下，粒子扩散运动的定性行为和相应的持续概率强烈依赖于环境的波动性质。在有界涨落的环境中，粒子表现出正常的扩散运动，扩散常数与持续概率简单相关。另一方面，在具有无界波动的介质中，扩散是超低的，并且颗粒的位移在对数时间尺度上增长。对于边缘波动的边界情况，扩散指数和持续指数都是非周期性的连续变化函数。还讨论了结果对无序介质和更高维度的扩展。@S1063-651X~99！04402-5#
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the transverse-field Ising model with inhomogeneous couplings, we obtain many analytical results for the random walk problem. In the absence of global bias the qualitative behavior of the diffusive motion of the particle and the corresponding persistence probability strongly depend on the fluctuation properties of the environment. In environments with bounded fluctuations the particle shows normal diffusive motion and the diffusion constant is simply related to the persistence probability. On the other hand, in a medium with unbounded fluctuations the diffusion is ultraslow and the displacement of the particle grows on logarithmic time scales. For the borderline situation with marginal fluctuations both the diffusion exponent and the persistence exponent are continuously varying functions of the aperiodicity. Extensions of the results to disordered media and to higher dimensions are also discussed. @S1063-651X~99!04402-5#