Quantized levitation by multiply-connected superconductors

A mesoscopic superconducting ring levitating a magnetic micro-sphere in a gravitational field exhibits two remarkable features: a) a small set of distinct, quantized, temperature dependent levitation and suspension states, b) a suppercurrent δ×H that differs from the quantum currentR(ψ*pψ). Quantized levitation, suspension, and trapped states exist when the micro-sphere is held in equilibrium by two fixed mesoscopic superconducting rings. The two independent fluxoid quantum numbers give rise to a complex set ofheight levels, and interlevel transitions at certain temperatures and gravitational fields.