A system for pumping or mixing a fluid F using a levitating, rotating pumpingor mixing element 812 and various other components for use in a pumping ormixing system are disclosed. The pumping or mixing element 812 is placed in afluid-containing vessel 810 in close proximity to a superconducting element818. A cooling source thermally linked to the superconducting element 818provides the necessary cooling to induce levitation in the pumping or mixingelement 812. The superconducting element 818 may be thermally isolated, suchthat the pumping or mixing element 812, the vessel 810, and any fluid Fcontained therein are not exposed to the cold temperatures required to producethe desired superconductive effects and the resulting levitation. By usingmeans external to the vessel to rotate and/or stabilize the pumping or mixingelement 812 levitating in the fluid F, including possibly rotating thesuperconducting elements 818 itself or moving it relative to the vessel 810,the desired effective pumping or mixing action may be provided.