空间相关衰减高斯随机势中的持续Sinai型扩散
Persistent Sinai type diffusion in Gaussian random potentials with decaying spatial correlations
摘要：
对数或西奈型亚扩散通常与随机力无序和非平稳势波动有关，其均方根振幅随距离增长。我们在这里表明，非常持久的，宏观的超低对数扩散也普遍出现在足够低的温度在平稳的高斯随机电位与空间衰减的相关性，已知存在于广泛的物理系统。结合大量的模拟结果与缩放的方法，我们阐明了这种不寻常的subdiffusion的物理机制。特别是，我们解释了为什么随着温度和/或时间的增长，第一次交叉发生标准，幂律次扩散，与时间相关的幂律指数，然后第二次交叉发生正常扩散与无序重正化扩散系数。有趣的是，最初的，名义上的超低速扩散原来是比通用的de Gennes-Baessler-Zwanzig极限的重整化正常扩散，这在物理上不能达到足够低的温度和/或强无序快得多。超慢扩散也是非遍历的，并显示出局部偏置现象。我们的简单标度理论不仅解释了我们的数值结果，但定性也有一个预测字符。
英文摘要：
Logarithmic or Sinai type subdiffusion is usually associated with random force disorder and non-stationary potential fluctuations whose root mean squared amplitude grows with distance. We show here that extremely persistent, macroscopic ultraslow logarithmic diffusion also universally emerges at sufficiently low temperatures in stationary Gaussian random potentials with spatially decaying correlations, known to exist in a broad range of physical systems. Combining results from extensive simulations with a scaling approach we elucidate the physical mechanism of this unusual subdiffusion. In particular, we explain why with growing temperature and/or time a first crossover occurs to standard, power-law subdiffusion, with a time-dependent power law exponent, and then a second crossover occurs to normal diffusion with a disorder-renormalized diffusion coefficient. Interestingly, the initial, nominally ultraslow diffusion turns out to be much faster than the universal de Gennes-Baessler-Zwanzig limit of the renormalized normal diffusion, which physically cannot be attained at sufficiently low temperatures and/or for strong disorder. The ultraslow diffusion is also non-ergodic and displays a local bias phenomenon. Our simple scaling theory not only explains our numerical findings, but qualitatively has also a predictive character.
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