Appearance of the Effective Mass in Polaron Models

Polarons are quasi-particles appearing in various physical models in condensed matter theory and can mathematically be described by coupling a charged particle to a quantum field of bosons. Physically, the interaction of the particle with the quantum field is expected to increase the effective mass of the polaron compared to the particle’s bare mass. Mathematically, there are various approaches for the definition and the analysis of the polaron’s effective mass based on semiclassical analysis, spectral theory or quantum dynamics. Our network, consisting of 16 young researchers, aims to link these a priori distinct definitions, by combining the expertise from functional analysis, probability theory and theoretical physics. Building on these links and thus the connection between diverse mathematical toolboxes, the goal is to jointly foster the progress on problems related to the effective mass such as the Landau-Pekar conjecture or the Cherenkov transition of the Bose polaron.