  The energy band structure of a rotating BEC with a link in a
quasi-one-dimensional torus and the role of dissipation is studied. Through
this study we are able to give a microscopic interpretation of hysteresis
recently observed in the experiment and we confirm that the hysteresis is the
result of the presence of metastable state. We consider of both the adiabatic
change and the instantaneous change of the rotation, and exhibit the
differences between them. It is found that the sharp and size of the hysteresis
loop change drastically with the strength of the link.
