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Resonance width oscillation in the bi-ripple ballistic electron waveguide

Interference of quasi bound states is studied in a ballistic electron ripple waveguide with two ripple cavities whose distance apart can be varied. This system is the waveguide analog of Dicke's model for two interacting atoms in a radiation field. Dicke's model has resonances whose widths change in an oscillatory manner as the distance between the atoms is varied. Resonances that form in a bi-ripple waveguide behave in a manner that has some similarity to Dicke's system, but also important differences. We numerically investigate the behavior of resonance widths in the waveguide as the distance between the two ripple cavities changes and we find that the resonance widths oscillate with variation of distance, but the coupling does not decrease as it does in Dicke's system. We discuss differences between our waveguide system and other systems showing the analogous of Dicke effect. We also study S-matrix pole trajectories and find that they rotate in counterclockwise direction on a circle in the complex energy plane.