Systems with many degrees of freedom: probalistic and constructive field theory methods

多自由度系统：概率论和构造性场论方法

• 批准号: 104281108
• 负责人: Professor Dr. Wolfgang König
• 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: Research Units
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/104281108?language=en
• 关键词: Systems; many; degrees; freedom; probalistic

Building on our progress of the first funding period, we will consider certain types of complex systems with many degrees of freedom and investigate new fundamental aspects of their behaviour. For bosonic many-particle systems, we want to find mathematical evidence for Bose-Einstein condensation at fixed temperature, and we want to study the effect of an additional attraction of the particles at positive distance at vanishing temperature. For fermionic many-particle systems, we want to extend the analysis we achieved in the first funding period to two-dimensional systems and to three-dimensional systems under a weaker diluteness assumption. In the parabolic Anderson model we want to study aging properties of the system and correlations in time, in the hope to investigate random hopping dynamics in general. Again, all these tasks require a systematic combination of probabilistic and analytic tools.

在第一个资助期的进展基础上，我们将考虑具有多个自由度的某些类型的复杂系统，并研究它们行为的新的基本方面。对于玻色子多粒子系统，我们想要找到玻色-爱因斯坦凝聚在固定温度下的数学证据，我们想要研究粒子在消失温度下正距离处的额外吸引力的影响。对于费米子多粒子系统，我们希望在较弱稀释假设下，将我们在第一个资助期所取得的分析扩展到二维系统和三维系统。在抛物型安德森模型中，我们希望研究系统的老化特性和时间相关性，以期研究一般的随机跳变动力学。同样，所有这些任务都需要概率和分析工具的系统结合。