Breakdown of `phase rigidity' and variations of the Fano effect in   closed Aharonov-Bohm interferometers
  Although the conductance of a closed Aharonov-Bohm interferometer, with a quantum dot on one branch, obeys the Onsager symmetry under magnetic field reversal, it needs not be a periodic function of this field: the conductance maxima move with both the field and the gate voltage on the dot, in an apparent breakdown of `phase rigidity'. These experimental findings are explained theoretically as resulting from multiple electronic paths around the interferometer ring. Data containing several Coulomb blockade peaks, whose shapes change with the magnetic flux, are fitted to a simple model, in which each resonant level on the dot couples to a different path around the ring. 
Amnon Aharony, Ora Entin-Wohlman, Tomohiro Otsuka, Shingo Katsumoto,   Hisashi Aikawa, Kensuke Kobayashi