Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model

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• 作者：Thomas Richthammer
• 刊名：Communications in Mathematical Physics
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：345
• 期：3
• 页码：1077-1099
• 全文大小：702 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Quantum Physics
  Quantum Computing, Information and Physics
  Complexity
  Statistical Physics
  Relativity and Cosmology
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0916
• 卷排序：345

文摘

The hard disk model is a 2D Gibbsian process of particles interacting via pure hard core repulsion. At high particle density the model is believed to show orientational order, however, it is known not to exhibit positional order. Here we investigate to what extent particle positions may fluctuate. We consider a finite volume version of the model in a box of dimensions 2n ×  2n with arbitrary boundary configuration, and we show that the mean square displacement of particles near the center of the box is bounded from below by c log n. The result generalizes to a large class of models with fairly arbitrary interaction.Communicated by H. Spohn