Hysteresis and metastability of Bose-Einstein-condensed clouds of atoms confined in ring potentials

We consider a Bose-Einstein-condensed cloud of atoms which rotate in a toroidal or annular potential. Assuming one-dimensional motion, we evaluate the critical frequencies associated with the effect of hysteresis and the critical coupling for stability of the persistent currents. We perform these calculations using both the mean-field approximation and the method of numerical diagonalization of the many-body Hamiltonian which includes corrections due to the finiteness of the atom number.