  We use the Bose-Hubbard Hamiltonian to study quantum fluctuations in
canonical equilibrium ensembles of bosonic Josephson junctions at relatively
high temperatures, comparing the results for finite particle numbers to the
classical limit that is attained as $N$ approaches infinity. We consider both
attractive and repulsive atom-atom interactions, with especial focus on the
behavior near the T=0 quantum phase transition that occurs, for large enough
$N$, when attractive interactions surpass a critical level. Differences between
Bose-Hubbard results for small $N$ and those of the classical limit are quite
small even when $N \sim 100$, with deviations from the limit diminishing as
1/N.
