The quantization of the extended canonical momentum in quantum materialsincluding the effects of gravitational drag is applied successively to the caseof a multiply connected rotating superconductor and superfluid. Experimentscarried out on rotating superconductors, based on the quantization of themagnetic flux in rotating superconductors, lead to a disagreement with thetheoretical predictions derived from the quantization of a canonical momentumwithout any gravitomagnetic term. To what extent can these discrepancies beattributed to the additional gravitomagnetic term of the extended canonicalmomentum? This is an open and important question. For the case of multiplyconnected rotating neutral superfluids, gravitational drag effects derived fromrotating superconductor data appear to be hidden in the noise of presentexperiments according to a first rough analysis.
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