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Steffen Polzer: Lower bound for the effective mass of the Fröhlich polaron
The Fröhlich polaron describes the slow movement of an electron in a polar crystal. A long open problem is the asymptotics of the effective mass of the polaron in the strong coupling limit. An application of the Feynman-Kac formula leads to Brownian motion perturbed by a pair potential. The point process representation introduced by Mukherjee and Varadhan represents this path measure as a mixture of Gaussian measures, the respective mixing measure can be interpreted in terms of a perturbed birth and death process. I will present joint work with Volker Betz in which we apply this representation in order to give a first quantitative lower bound on the effective mass. I will additionally show how the renewal structure of the underlying point processes can be applied in order to study the whole energy-momentum relation.