  The quantization of the extended canonical momentum in quantum materials
including the effects of gravitational drag is applied successively to the case
of a multiply connected rotating superconductor and superfluid. Experiments
carried out on rotating superconductors, based on the quantization of the
magnetic flux in rotating superconductors, lead to a disagreement with the
theoretical predictions derived from the quantization of a canonical momentum
without any gravitomagnetic term. To what extent can these discrepancies be
attributed to the additional gravitomagnetic term of the extended canonical
momentum? This is an open and important question. For the case of multiply
connected rotating neutral superfluids, gravitational drag effects derived from
rotating superconductor data appear to be hidden in the noise of present
experiments according to a first rough analysis.
