  We consider the open quantum random walks on the crystal lattices and
investigate the central limit theorems for the walks. On the integer lattices
the open quantum random walks satisfy the central limit theorems as was shown
by Attal, {\it et al}. In this paper we prove the central limit theorems for
the open quantum random walks on the crystal lattices. We then provide with
some examples for the Hexagonal lattices. We also develop the Fourier analysis
on the crystal lattices. This leads to construct the so called dual processes
for the open quantum random walks. It amounts to get Fourier transform of the
probability densities, and it is very useful when we compute the characteristic
functions of the walks. In this paper we construct the dual processes for the
open quantum random walks on the crystal lattices providing with some examples.
