Superdiffusive nonequilibrium motion of an impurity in a Fermi sea

We treat the nonequilibrium motion of a single-impurity atom in a low-temperature single-species Fermi sea, interacting via a contact interaction. In the nonequilibrium regime, the impurity does a superdiffusive geometric random walk where the typical distance traveled grows with time as ∼td ^/(d ⁺1 ⁾ for the d-dimensional system with d2. For nonzero temperature T, this crosses over to diffusive motion at long times with diffusivity D∼T ^-(d ^-1 ^)/2. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.