From microscopic to macroscopic scales: effective evolution equations of many interacting particles. |
Chiara Saffirio, Universität Basel |
Freitag, 2024-06-14 13:30Uhr |
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Systems of interacting particles describing notable physical phenomena, such as time-irreversibility, Bose-Einstein condensation, superconductivity or superfluidity, represent a veritable challenge for mathematicians and physicists. They exhibit a daunting complexity, which renders the exact many-body theory non-approachable, not only from a mathematical viewpoint, but also for computer experiments and simulations. Therefore, an approximate description using effective macroscopic models is highly useful, and the rigorous study of the regime of validity of such approximations is of primary importance in mathematical physics. In this talk, I will present several settings leading to different effective kinetic equations and then I will focus on the mean-field regime for quantum particle systems, highlighting recent significant progress in the mathematical understanding of these systems. |