Transmission coefficient for a point scatterer at specific energies is affected by the presence of the scatterer but independent of the scatterer's characteristics

We calculate the exact transmission coefficients of a quantum wire in the presence of a single point defect at the wire's cutoff frequencies. We show that at these frequencies while the conductance pattern (i.e., the scattering) is strongly affected by the presence of the defect, the pattern is totally independent of the defect's characteristics (i.e., the defect that caused the scattering cannot be identified from that pattern). The change in the conduction pattern can cause universal attraction and/or repulsion forces between two parallel conducting wires.