  Motivated by the experiment of electrostatic conveyor belt for indirect
excitons [A. G. Winbow, \textit{et al.}, Phys. Rev. Lett. \textbf{106}, 196806
(2011)], we study the exciton patterns for understanding the exciton dynamics.
By analyzing the exciton diffusion, we find that the patterns mainly come from
the photoluminescence of two kinds of excitons. The patterns near the laser
spot come from the hot excitons which can be regarded as the classical
particles. However, the patterns far from the laser spot come from the cooled
excitons or coherent excitons. Taking into account of the finite lifetime of
Bosonic excitons and of the interactions between them, we build a
time-dependent nonlinear Schr\"{o}dinger equation including the non-Hermitian
dissipation to describe the coherent exciton dynamics. The real-time and
imaginary-time evolutions are used alternately to solve the Schr\"{o}dinger
equation in order to simulate the exciton diffusion accompanied with the
exciton cooling in the moving lattices. By calculating the escape probability,
we obtain the transport distances of the coherent excitons in the conveyor
which are consistent with the experimental data. The cooling speed of excitons
is found to be important in the coherent exciton transport. Moreover, the
plateau in the average transport distance cannot be explained by the dynamical
localization-delocalization transition induced by the disorders.
