  A superglass is a phase of matter which is characterized at the same time by
superfluidity and a frozen amorphous structure. We introduce a model of
interacting bosons in three dimensions that displays this phase unambiguously
and that can be analyzed exactly or using controlled approximations. Employing
a mapping between quantum Hamiltonians and classical Fokker-Planck operators,
we show that the ground state wavefunction of the quantum model is proportional
to the Boltzmann measure of classical hard spheres. This connection allows us
to obtain quantitative results on static and dynamic quantum correlation
functions. In particular, by translating known results on the glassy dynamics
of Brownian hard spheres we work out the properties of the superglass phase and
of the quantum phase transition between the superfluid and the superglass
phase.
