Quantum particle on a fermionic surface: Mapping the fermion bath to a boson bath

This paper investigates the quantum dynamics of a particle on a fermionic surface, e.g., an ion on a metallic surface. The question addressed is whether mapping from a fermion bath to a boson bath can be achieved in this case, as has been shown for several other cases. Using a previously established method, we demonstrate explicitly that in a certain limit, the influence of the coupling between the particle and the bulk fermions is the same as if the particle interacts linearly with an ohmic boson bath, regardless of the coupling strength. The obtained viscosity η is expressed explicitly in terms of the scattering phase shift at the Fermi surface; in particular, the s-wave scattering has no effects on the dynamics.