Dirac impurity in a Luttinger liquid
Lorenzo Gotta (University of Geneva)
We consider a linearly-dispersing quantum impurity interacting through a contact density-density term with a one-dimensional superfluid described by Luttinger liquid theory. We employ field-theoretical tools to characterize the impurity dynamics by calculating approximate expressions for the single-particle Green’s function and the time evolution of the density profile. We discover the existence of two different dynamical regimes, separated by a change in the relative magnitude of the impurity velocity and of the sound velocity. When the latter is smaller than the former, the impurity behavior is dominated by the quasiparticle universality class, signaled by the existence of a well-defined lifetime. In the opposite case, the dynamical properties of the mobile impurity are instead interpreted as a manifestation of Anderson’s orthogonality catastrophe, and result in an enhanced robustness of free impurity propagation with respect to the quasiparticle regime. Preliminary results on the effects of a finite-temperature bath on the impurity probes are additionally presented.