Momentum Evolution Numerics of an Impurity in a Quantum Quench

A discussion on the momentum evolution of an impurity interacting via a finite delta potential repulsion with a non-interacting fermionic background gas is presented. It has recently been shown that the momentum evolution of this system displays two interesting features, namely a non-zero thermalised value and a long-lived quantum mechanical oscillation around this plateau named "quantum flutter" [Mathy, Zvonarev, Demler, Nat. Phys. 2012]. We discuss revivals in the momentum of the impurity, which have been seen before but not yet thoroughly investigated. Subsequently it is shown the quantum flutter and revivals are caused by disjoint sets of eigenstate transitions, and this fact is used to interpret some of their aspects. This attribution of momentum features to different eigenstate subsets allows quantitative reproduction of these features with much less computational expense than has so far been possible. Finally some results on the distribution of the momentum of eigenstates and their relation to the momentum of the impurity once the system has been thermalised are presented along with a discussion on the time averaged infinite time value of the momentum and its comparison to different eigenstate subsets.