Conductance of a quantum wire with an attractive smooth impurity potential

We calculate the conductance through an attractive smoothly varying impurity potential in a quantum wire using the Lippmann-Schwinger equation. The impurity has a decay length along the propagation direction while it is localized along the transverse direction. It is shown that the conductance versus Fermi energy exhibits multiple resonant dips which are due to the creation of quasibound states and their interaction with the continuum states. By varying the size of the impurity the quasibound states evolve into highly localized states with enhanced lifetime