Non-perturbative approach to backscattering off a dynamical impurity in   1D Fermi systems
  We investigate the problem of backscattering off a time-dependent impurity in a one-dimensional electron gas. By combining the Schwinger-Keldysh method with an adiabatic approximation in order to deal with the corresponding out of equilibrium Dirac equation, we compute the total energy density (TED) of the system. We show how the free fermion TED is distorted by the backscattering amplitude and the geometry of the impurity. 
Daniel G. Barci, L. Moriconi, M. Moriconi, Carlos M. Na\'on, Mariano   J. Salvay