  We study the equilibrium and non-equilibrium properties of strongly
interacting bosons on a lattice in presence of a random bounded disorder
potential. Using a Gutzwiller projected variational technique, we study the
equilibrium phase diagram of the disordered Bose Hubbard model and obtain the
Mott insulator, Bose glass and superfluid phases. We also study the non
equilibrium response of the system under a periodic temporal drive where,
starting from the superfluid phase, the hopping parameter is ramped down
linearly in time, and back to its initial value. We study the density of
excitations created, the change in the superfluid order parameter and the
energy pumped into the system in this process as a function of the inverse ramp
rate $\tau$. For the clean case the density of excitations goes to a constant,
while the order parameter and energy relaxes as $1/\tau$ and $1/\tau^2$
respectively. With disorder, the excitation density decays exponentially with
$\tau$, with the decay rate increasing with the disorder, to an asymptotic
value independent of the disorder. The energy and change in order parameter
also decrease as $\tau$ is increased.
