  We study the rotation of atoms in one-dimensional lattice rings. In
particular, the "fast mode", where the ground state atoms rotate faster than
the stirring rotating the atoms, is studied both analytically and numerically.
The conditions for the transition to the fast mode are found to be very
different from that in continuum rings. We argue that these transition
frequencies remain unchanged for bosonic condensates described in a mean field.
We show that Fermionic interaction and filling factor have a significant effect
on the transition to the fast mode, and Pauli principle may suppress it
altogether.
