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We study the stability and dynamics of an ultra-cold bosonic gas trapped in atoroidal geometry and driven by rotation, in the absence of dissipation. Wefirst delineate, via the Bogoliubov mode expansion, the regions of stabilityand the nature of instabilities of the system for both repulsive and attractiveinteraction strengths. To study the response of the system to variations in therotation rate, we introduce a "disorder" potential, breaking the rotationalsymmetry. We demonstrate the breakdown of adiabaticity as the rotation rate isslowly varied and find forced tunneling between the system's eigenstates. Thenon-adiabaticity is signaled by the appearance of a swallow-tail loop in thelowest-energy level, a general sign of hysteresis. Then, we show that thissystem is in one-to-one correspondence with a trapped gas in a double-wellpotential and thus exhibits macroscopic quantum self-trapping. Finally, we showthat self-trapping is a direct manifestation of the behavior of thelowest-energy level.

Bose-Einstein condensates in toroidal traps: instabilities, swallow-tail loops, and self-trapping