Seminarium Fizyki Materii Skondensowanej

The polaron model is a basic model of quantum field theory describing a single particle interacting with a bosonic field. It arises in many physical contexts. We are mostly concerned with models applicable in the context of an impurity atom in a BEC as well as the problem of electrons in polar crystals.We investigate rigorously the ground state of the model at fixed momentum and for large values of the coupling constant. In the strong coupling regime, the bosonic field is expected to behave purely classically. Accordingly, the effective mass of the polaron at strong coupling is conjectured to be asymptotically equal to the one obtained from the semiclassical counterpart of the problem, first studied by Landau and Pekar in the 1940s. For polaron models with regularized form factors and phonon dispersion relations of superfluid type, i.e., linear for small wavenumbers as in the interacting Bose gas, we prove that for a large window of momenta below the radiation threshold, the energy-momentum relation as strong coupling is indeed essentially parabolic with semi-latus rectum equal to the Landau-Pekar effective mass as expected. For the Froehlich polaron describing electrons in polar crystals where the dispersion relation is of the optical type and the form factor is formally UV-singular due to the nature of the point charge-dipole interaction, we are able to give the corresponding upper bound. In contrast to the regular case, this requires the inclusion of the quantum fluctuations of the phonon field, which makes the problem considerably more difficult.During the talk, priority will be given to a healthy balance between rigor and physical intuition.Based on joint works with David Mitrouskas and Robert Seiringer.