Backscattering off a dynamical impurity in one-dimensional Fermi   systems: A perturbative computation
  We investigate the problem of backscattering off a time-dependent and spatially extended barrier in a one-dimensional electron gas. By performing a perturbative expansion in the backscattering amplitude, we compute the total energy density of the system. We show how the free fermion spectrum and the conductance of the system are affected by the interplay between dynamical and geometrical properties of the impurity. 
Carlos M. Na\'on and Mariano J. Salvay