Classical and quantum kinetic equations (A02)

• Subject Area: Mathematics
• Term: since 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 211504053

The goal of this project is to study both the rigorous derivation of several types of kinetic equations and the properties of their solutions. Specifically, we are interested in the derivation of kinetic equations for Lorentz gases starting from the equation for the Hamiltonian dynamics of a particle in a random distribution of scatterers. We will also consider the derivation of the Boltzmann equation for bosons starting from a stochastic process (Kac model) with Bose-Einstein statistics. Moreover, we will study the different possible long-time behaviors of so-called homoenergetic solutions of the Boltzmann equation which describe the dynamics of Boltzmann gases in open systems. Finally, we will analyse the properties of solutions of Vlasov-Fokker-Planck-type equations arising in the study of polymer distributions.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1060: The Mathematics of Emergent Effects
• Applicant Institution: Rheinische Friedrich-Wilhelms-Universität Bonn
• Project Head: Professor Dr. Juan José López Velázquez