Heavy Particle in a d-Dimensional Fermionic Bath: A Strong Coupling Approach

We investigate the low temperature behavior of a heavy particle in a fermionic bath. Two competing effects dominate the physics: a shakeup of the Fermi sea (orthogonality catastrophe) destroys the coherence, while the recoil of the particle tends to restore it by reducing the available phase space for scattering events. An effective action is considered which exactly implements these two aspects. In one dimension the coherence of the particle is destroyed—the propagator decays algebraically for long times. In two and higher dimensions coherent propagation survives.