The statistical mechanics of the interlacement point process

交错点过程的统计力学

• 批准号: 443849332
• 负责人: Professor Dr. Alexander Drewitz
• 金额: --
• 依托单位: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/443849332?language=en
• 关键词: statistical; mechanics; interlacement; point; process

In this project, we will lay the foundations for a new theory of statistical mechanics for point processes of random paths in Euclidean space of unbounded and even infinite lengths. The main novelty will be a proper treatment of the level-three large deviations for the empirical stationary field in large boxes, including a description of the rate function as a new kind of limiting entropy density. This will make possible a mathematically sound geometric description of the interacting Bose gas in the condensation regime in the thermodynamic limit -- this is our main example and the driving force of this research. We plan to describe the condensate rigorously in terms of an interacting interlacement process. The understanding we expect to obtain might also be useful in the context of the open problem of finding a proof for the occurrence of Bose--Einstein condensation.

在这个项目中，我们将为无界甚至无限长的欧氏空间中随机路径的点过程的一个新的统计力学理论奠定基础。主要的新奇之处将是对大盒子中经验稳态场的三级大偏差进行适当的处理，包括将速率函数描述为一种新的极限熵密度。这将使热力学极限下凝聚区相互作用玻色气体的数学几何描述成为可能--这是我们的主要例子，也是这项研究的驱动力。我们计划用一个相互交错的过程来严格地描述凝析油。我们期望得到的理解在寻找玻色-爱因斯坦凝聚发生的证据这一悬而未决的问题的背景下也可能有用。