Seminarium Fizyki Materii Skondensowanej

Despite being introduced by Landau almost 90 years ago, there are still some basic aspects of the polaron that are not fully understood from a mathematical point of view. In particular, the connection between Pekar's semi-classical analysis, in which the field is treated as a classical variable, and the Fröhlich model at strong coupling has posed interesting mathematical problems. In this talk, we will present recent results concerning the spectrum of the Fröhlich Hamiltonian. These include an asymptotic formula for the energy momentum relation and the abundance of eigenvalues below the essential spectrum at fixed total momentum. If time permits, we will also discuss the dynamical properties of the polaron. For suitable initial conditions, the quantum dynamics can be approximated by the time-dependent Landau-Pekar equations, a set of coupled partial differential equations that describe the evolution of an electron in a slowly varying classical polarization field. The talk is based on joint work with J. Lampart, N. Leopold, K. Mysliwy, S. Rademacher, B. Schlein and R. Seiringer.