A SINGLE SCATTERER IN A QUANTUM WIRE - COMPACT REFORMULATION OF SCATTERING AND TRANSMISSION

Employing the concept of backscattering from the lateral confinement, all multiple scattering effects between scatterer and walls are condensed in a renormalized scattering amplitude. This allows a very compact discussion of resonant states and their pronounced effect on the transmittivity and of ideal transparency just below energetic channel thresholds. The role of the local density of states (LDOS) within the empty wire is exhibited, too. As final result, the conductance is related by a simple formula to the scattering amplitude, the LDOS and an amplitude for backscattering from the lateral confinement.