  When a one dimensional (1D) ring-stub system is coupled to an electron
reservoir, the states acquire a width (or broadening characterized by poles in
the complex energy plane) due to finite life time effects. We show that this
broadening is limited by anti-resonances due to the stub. The differences in
level broadening in presence and absence of anti-resonance is exemplified by
comparison to a 1D ring coupled to an infinite reservoir. We also show that the
anti-resonances due to the stub has an anchoring effect on the poles when a
magnetic flux through the ring is varied. This will have implication on change
in distribution of the poles in disordered multichannel situation as magnetic
flux is varied.
