Near-threshold-energy conductance of a thin wire

We show (1) that a single impurity can have an extremely strong impact on the conductance of a thin wire; (2) that in such a thin wire a couple of two-dimensional impurities may be responsible to strong resonances. (3) Further, we study rough wire transmission in the low-energy regime. We obtain strong localization behavior (Formula presented) [L is the wire length and (Formula presented) ω is the particle energy and (Formula presented) is the threshold energy of a similar wire but without the roughness]. We also show that for very long wires the difference between the threshold energy for transmission (Formula presented) and (Formula presented) increases logarithmically with the wire length (Formula presented)