Zero temperature limit for interacting Brownian particles. I. Motion of a single body

• 成果类型: Article
• 署名作者: Funaki, T
• 署名单位: University of Tokyo
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000180
• 发表日期: 2004
• 页码: 1201-1227
• 关键词: rigidity; graphs

摘要

We consider a system of interacting Brownian particles in R-d with a pairwise potential, which is radially symmetric, of finite range and attains a unique minimum when the distance of two particles becomes a > 0. The asymptotic behavior of the system is studied under the zero temperature limit from both microscopic and macroscopic aspects. If the system is rigidly crystallized, namely if the particles are rigidly arranged in an equal distance a, the crystallization is kept under the evolution in macroscopic time scale. Then, assuming that the crystal has a definite limit shape under a macroscopic spatial scaling, the translational and rotational motions of such shape are characterized.