  We investigate the disorder effect on coherent fraction and the quantum phase
transition of ultracold dilute Bose gases trapped in disordered optical
lattices. Within the framework of Bogoliubov theory, an analytical expression
for the particle density is derived and the dependence of coherent fraction on
disorder strength as well as on lattice depth is discussed. In weak disorder
regime, we find a decreased sensitivity of coherent fraction to disorder with
the increase of on-site interaction strength. For strong disorder, the quantum
phase boundary between superfluid phase and Bose glass phase in the disordered
Bose-Hubbard system in weak interaction regime is discussed qualitatively. The
obtained phase diagram is in agreement with the empirical square-root law. The
dependence of the corresponding critical value of the disorder strength on
optical lattice depth is presented as well, and may serve as a reference object
for possible experimental investigation.
