Quantization of superflow circulation and magnetic flux with a tunable offset

Quantization of superflow circulation and of magnetic flux are considered for systems, such as superfluid (Formula presented) and unconventional superconductors, having nonscalar order parameters. The circulation is shown to be the anholonomy in the parallel transport of the order parameter. For multiply-connected samples free of distributed vorticity, circulation and flux are predicted to be quantized, but generically to nonintegral values that are tunably offset from integers. This amounts to a version of Aharonov-Bohm physics. Experimental settings for testing these issues are discussed.