We present a theoretical treatment of the surprisingly large damping observed

recently in one-dimensional Bose-Einstein atomic condensates in optical

lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB)

calculations can describe qualitatively the main features of the damping

observed over a range of lattice depths. We also derive a formula of the

fluctuation-dissipation type for the damping, based on a picture in which the

coherent motion of the condensate atoms is disrupted as they try to flow

through the random local potential created by the irregular motion of

noncondensate atoms. We expect this irregular motion to result from the

well-known dynamical instability exhibited by the mean-field theory for these

systems. When parameters for the characteristic strength and correlation times

of the fluctuations, obtained from the HFB calculations, are substituted in the

damping formula, we find very good agreement with the experimentally-observed

damping, as long as the lattice is shallow enough for the fraction of atoms in

the Mott insulator phase to be negligible. We also include, for completeness,

the results of other calculations based on the Gutzwiller ansatz, which appear

to work better for the deeper lattices.