Periodic Reporting for period 4 - AQUAMS (Analysis of quantum many-body systems)
Reporting period: 2021-04-01 to 2022-03-31
The goal of this project is the development of new mathematical tools for dealing with complex problems in many-body quantum systems. New mathematical methods lead to different points of view and thus increase our understanding of physical systems. From the point of view of mathematical physics, there has been significant progress in the last few years in understanding the interesting phenomena occurring in quantum gases, and the goal of this project is to investigate some of the key issues that remain unsolved. Due to the complex nature of the problems, new mathematical ideas and methods will have to be developed for this purpose.
During the course of this project, several important open problem could be solved. These include the existence of Bose-Einstein condensation at positive temperature for dilute trapped gases, the stability analysis of an impurity in a Fermi gas, or the confirmation of the validity of the Gellmann-Bruckner formula for the correlation energy of a weakly interacting Fermi gas, just to mention a few. The tools and methods developed in the course of these projects can be expected to to trigger further advances in the field in the future.