Many-body systems, interacting brownian motions, and functional integrals

多体系统、相互作用的布朗运动和功能积分

• 批准号: 20968246
• 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: 2006
• 资助国家: 德国
• 起止时间: 2005-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/20968246?language=en
• 关键词: Many; body; systems; interacting; brownian

In this project we investigate the low-temperature behaviour of dilute quantum many-particle models. Our main interest is in understanding the dependence of the free energy density and correlation functions in the Gross-Pitaevskii limit, as well as generalisations of this limit which correspond to slightly larger densities. We consider both the canonical and the grand canonical ensemble. The former is studied via the interacting Brownian motion representation, using large deviations techniques, the latter via coherent-state functional integrals, using techniques from constructive quantum field theory. We also aim to investigate the connections between these two approaches.

在这个项目中，我们研究了稀疏量子多粒子模型的低温行为。我们的主要兴趣是了解Gross-Pitaevskii极限中自由能密度和关联函数的依赖关系，以及该极限对应于稍大密度的推广。我们既考虑正则系综又考虑大正则系综系综.前者通过相互作用的布朗运动表示，使用大偏差技术，后者通过相干态泛函积分，使用构造性量子场论的技术来研究。我们还打算调查这两种方法之间的联系。