  Properties of bosonic atoms in small systems with a periodic quasi
one-dimensional circular toroidal lattice potential subjected to rotation are
examined by performing exact diagonalization in a truncated many body space.
The expansion of the many-body Hamiltonian is considered in terms of the first
band Bloch functions, and no assumption regarding restriction to
nearest-neighbor hopping (tight-binding approximation) is involved. A finite
size version of the zero temperature phase diagrams of Fisher et al.
\cite{Fisher} is obtained and the results, in remarkable quantitative
correspondence with the results available for larger systems, discussed. Ground
state properties relating to superfluidity are examined in the context of
two-fluid phenomenology. The basic tool, consisting of the intrinsic inertia
associated with small rotation angular velocities in the lab frame, is used to
obtain ground state `superfluid fractions' numerically. They are analytically
associated with one-body, uniform solenoidal currents in the case of the
adopted geometry. These currents are in general incoherent superpositions of
contributions from each eigenstate of the associated reduced one-body
densities, with the corresponding occupation numbers as weights. Full coherence
occurs therefore only when only one eigenstate is occupied by all bosons. The
obtained numerical values for the superfluid fractions remain small throughout
the parameter region corresponding to the `Mott insulator to superfluid'
transition, and saturate at unity only as the lattice is completely smoothed
out.
