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

点击翻译按钮获取中文摘要

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.