On macroscopic quantum phenomena associated with the quantised Hall effect

The relation between the quantised Hall conductance and other macroscopic quantum effects is discussed. Under the appropriate conditions, a multiply connected system exhibiting the quantised Hall effect may be sensitive to fractions of magnetic flux quanta through its opening. Thus, phenomena similar to fluxoid quantisation and the AC Josephson effect are possible in these systems. The latter effect may appear simply as an AC component on top of the quantised Hall current, as well as one parallel to the Hall voltage. The magnitudes of these effects are estimated and conditions for their observation formulated. Subtleties associated with the Hall voltage source are discussed.