# Classical and Quantum Mechanical Models of Many-Particle Systems

### Anton Arnold

Technische Universität Wien, Austria### Eric A. Carlen

Rutgers University, Piscataway, United States### Laurent Desvillettes

CMLA-ENS, Cachan, France

## Abstract

This meeting was focused on recent results on the mathematical analysis of many-particle systems, both classical and quantum-mechanical in scaling regimes such that the methods of kinetic theory can be expected to apply. Thus, the Boltzmann equation is in many ways the central equation investigated in much of the research presented and discussed at this meeting, but the range of topics naturally extended from this center to include other non-linear partial differential and integro-differential equations, especially macroscopic/fluid-dynamical limits of kinetic equations modeling the dynamics of many-particle systems. A significant subset of the talks focused on propagation of chaos, and the validation and derivation of kinetic equations from underlying stochastic particle models in which there has been much progress and activity. Models were discussed with applications not only in physics, but also engineering, and mathematical biology. While there were a number of new participants, especially younger researchers, an interesting aspect of the conference was the number of talks presenting progress that had its origins in the previous meeting in this series held in 2010.

## Cite this article

Anton Arnold, Eric A. Carlen, Laurent Desvillettes, Classical and Quantum Mechanical Models of Many-Particle Systems. Oberwolfach Rep. 10 (2013), no. 4, pp. 3305–3378

DOI 10.4171/OWR/2013/57