Classical and Quantum Mechanical Models of Many-Particle Systems (online meeting)

Abstract

The collective behaviour of many-particle systems is a common denominator in the challenges of a highly diverse range of applications: from classical problems in Physics (gas dynamics e.g. Boltzmann's equation, plas-ma dynamics e.g. various Vlasov equations, semiconductors, quantum mechanics) to current models in biology (kinetic models for collective interaction e.g. swarming, evolution of trait-structured species) to rising topics in social sciences (opinion formation, crowding phenomena) and economics (wealth distribution, mean-field games).\ Key mathematical questions concern the analysis (global-in-time wellposedness, regularity), rigorous scaling resp. macroscospic limits (model reduction from many-particle models to mean-field/mesoscopic descriptions to macroscopic evolutions), efficient and asymptotic preserving numerical methods and qualitative results (e.g. large-time equilibration).