Quantum flutter from the nonlinear Luttinger liquid perspective

Quantum flutter is a ubiquitous phenomenon which can be observed from the fast moving impurity injected into a fermionic or bosonic medium of quantum liquid. In this scenario, one usually considers a medium of a fully polarized state and injects a spin-flipped impurity as the initial state. When the initial velocity of the impurity is beyond the intrinsic sound velocity of the medium, the impurity momentum dramatically exhibits a long-lived periodic oscillation with the periodicity remaining invariant with respect to the initial velocity. In this paper, we show that such a novel phenomenon can be explained by a linear Luttinger liquid coupled to a deep hole in the Fermi sea. Once the deep hole excitations are involved and the impurity momentum surpasses the Fermi momentum, the propagator thus displays a periodic oscillation after a quick relaxation decay. The oscillation periodicity is solely determined by the energy of the deepest hole excitation. Our result provides deep insights into the dynamical behavior of quantum impurities immersed into one-dimensional quantum liquids.