Abstract
The quantum fluctuation effects on the center-of-mass (c.m.) motion of a condensate in a parabolic potential in a one-dimensional optical lattice were investigated. The study was carried out by using the truncated Wigner approximation (TWA). The mean field results were reproduce in the strong tunnelling limit with a sharp dynamical transition at the critical displacement. The results show that the quantum fluctuations were very important even far from the superfluid-to-insulator transition boundary.