In this connection, we mention that

In this connection, we mention that the development of the theory of aperiodic conductance fluctuations (discussed in Section II.C) has been much stimulated by their observation in metal rings by Webb et al.,165 in the course of their search for the Aharonov-Bohm effect. The reason that aperiodic fluctuations are observed in rings (in addition to periodic oscillations) is that the magnetic field penetrates the width of the arms of the ring and is not confined to its interior. By fabricating rings with a large ratio of radius r to width W, researchers have proven it is possible to separate190 the magnetic field scales of the periodic and aperiodic oscillations (which are given by a field interval of order h/er2 and h/eWl, respectively). The penetration of the magnetic field in the arms of the ring also leads to a broadening of the peak in the Fourier transform at the e/h and 2e/h periodicities, associated with a distribution of enclosed flux. The width of the Fourier peak can be used as a estimate for the width of the arms of the ring. In addition, the nonzero field in the arms of the ring also leads to a damping of the amplitude of the ensemble-averaged h/2e oscillations when the flux through the arms is sufficiently large to suppress weak localization.191