Superdiffusive nonequilibirum transport of an impurity in a Fermi sea

We discuss a nonequilibrium transport of a single impurity atom immersed in a low-temperature Fermi sea with a short range interaction. We find that the impurity does a superdiffusive geometric random walk in which the characteristic momentum decay rate shows a quartic decrease in its momentum in three dimension. Then, we construct a master equation and its scaled form that governs the time evolution of the impurity. Next, we discuss two dimensional case in which the momentum decay rate decreases with the third power of its momentum.