  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.
