Phase and periodicity of Aharonov-Bohm oscillations: effect of channel mixing

We take a negative delta function impurity in one arm of a quasi one dimensional Aharonov-Bohm ring and demonstrate abrupt phase changes across a quasi bound state of the negative delta function potential. We give a new mechanism for conductance oscillations with the strength of the negative delta potential. We also show that coupling to evanescent modes can result in a $hc/2e$ flux periodicity at certain energies. These observations were made in a recent ingenious experiment by D. Mailly et al [1].