Subdiffusion, Anomalous Diffusion and Propagation of a Particle Moving in Random and Periodic Media

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• 作者：Shradha Mishra ; Sanchari Bhattacharya ; Benjamin Webb…
• 关键词：Lorentz lattice gas ; Subdiffusion ; Self ; avoiding walk ; Fractal dimension ; Flipping scatterers
• 刊名：Journal of Statistical Physics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：162
• 期：4
• 页码：855-868
• 全文大小：1,650 KB
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• 作者单位：Shradha Mishra (1) (2)
  Sanchari Bhattacharya (2)
  Benjamin Webb (3)
  E. G. D. Cohen (4)
  
  1. Department of Physics, Indian Institute of Technology (BHU), Varanasi, UP, 221005, India
  2. Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata, 700098, India
  3. Department of Mathematics, Brigham Young University, 308 TMCB, Provo, UT, 84602, USA
  4. The Rockefeller University, 1230 York Avenue, New York, NY, 10021, USA
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

We investigate the motion of a single particle moving on a two-dimensional square lattice whose sites are occupied by right and left rotators. These left and right rotators deterministically rotate the particle’s velocity to the right or left, respectively and flip orientation from right to left or from left to right after scattering the particle. We study three types of configurations of left and right rotators, which we think of as types of media, through with the particle moves. These are completely random (CR), random periodic (RP), and completely periodic (CP) configurations. For CR configurations the particle’s dynamics depends on the ratio r of right to left scatterers in the following way. For small \(r\simeq 0\), when the configuration is nearly homogeneous, the particle subdiffuses with an exponent of 2/3, similar to the diffusion of a macromolecule in a crowded environment. Also, the particle’s trajectory has a fractal dimension of \(d_f\simeq 4/3\), comparable to that of a self-avoiding walk. As the ratio increases to \(r\simeq 1\), the particle’s dynamics transitions from subdiffusion to anomalous diffusion with a fractal dimension of \(d_f\simeq 7/4\), similar to that of a percolating cluster in 2-d. In RP configurations, which are more structured than CR configurations but also randomly generated, we find that the particle has the same statistic as in the CR case. In contrast, CP configurations, which are highly structured, typically will cause the particle to go through a transient stage of subdiffusion, which then abruptly changes to propagation. Interestingly, the subdiffusive stage has an exponent of approximately 2/3 and a fractal dimension of \(d_f\simeq 4/3\), similar to the case of CR and RP configurations for small r. Keywords Lorentz lattice gas Subdiffusion Self-avoiding walk Fractal dimension Flipping scatterers