Theory of hopping motion of a heavy particle interacting with a degenerate electron gas

A heavy particle moving by hopping on a lattice is considered. The screening and assisted hopping due to the electrons result in logarithmic contributions to the scattering amplitude. In the study of a one-dimensional model, scaling similar to the anisotropic antiferromagnetic Kondo problem is found. The large-scaled couplings reduce the width of the heavy particle band essentially. The results obtained hold also for heavy particles forming a degenerate Fermi gas.