Emergence of Time-Dependent Point Interactions in Polaron Models

We study the dynamics of three-dimensional polaron - a quantum particle coupled to bosonic fields in quasi-classical regime. In this case are very intense and corresponding degrees freedom can be treated semiclassically. prove that such regime effective for particles is approximated by one generated time-dependent point interaction, i.e., singular perturbation Laplacian supported point. As by-product, we also show unitary interaction strong operator topology Schr\"{o}dinger operators with suitably rescaled regular potentials.