Abstract:
A long standing open problem is the asymptotics of the effective mass for the Froehlich polaron in the strong coupling limit. Already Feynman formulated it in terms of path integrals, which leads to a three dimensional Brownian motion with an attractive path interaction with a singular interaction kernel.
In the celebrated paper by Donsker and Varadhan (Comm Pure Appl Math, 1983), the asymptotics of the free energy is considered. The effective mass is however closely tied to the path behavior which is more delicate. In a heuristic derivation by Spohn (Phys Rev B, 1986) the problem is related to the behavior of a stochastic process, Spohn called the "Pekar process". The problem about the asymptotics of the effective mass is mathematically still open. In the work with Koenig and Mukherjee (Comm Pure Appl Math 2017), we construct rigorously the Pekar process as the asymptotic limit of the Brownian motion with the singular pair interaction, and we discuss the conjectured relation with the original problem.
This is joint work with Wolfgang Koenig and Chiranjib Mukherjee.
Biography:
Erwin Bolthausen graduated at the ETH in Zürich receiving his PhD in mathematics in 1973. After a postdoc position in Konstanz, Germany, he moved in 1978 to Frankfurt as an associate professor, and in 1979 as a full professor to the Technical University in Berlin. In 1990 he took up a position at the University of Zürich, where he retired 2012. He is a member of the German Academy of Science Leopoldina, and he received the Humboldt Forschungspreis in 2008. He was an invited speaker at the ICM in Beijing 2002. His main research interests focus on random media, including random walks in random environments, and spin glasses.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai