  We consider a small ensemble of Bose atoms in a ring optical lattice with
weak disorder. The atoms are assumed to be initially prepared in a superfluid
state with non-zero quasimomentum and, hence, may carry matter current. It is
found that the atomic current persists in time for a low value of the
quasimomentum but decays exponentially for a high (around one quater of the
Brillouin zone) quasimomentum. The explanation is given in terms of low- and
high-energy spectra of the Bose-Hubbard model, which we describe using the
Bogoliubov and random matrix theories, respectively.
