  We investigate the wave packet dynamics for a one-dimensional incommensurate
optical lattice with a special on-site potential which exhibits the mobility
edge in a compactly analytic form. We calculate the density propagation,
long-time survival probability and mean square displacement of the wave packet
in the regime with the mobility edge and compare with the cases in extended,
localized and multifractal regimes. Our numerical results indicate that the
dynamics in the mobility-edge regime mix both extended and localized features
which is quite different from that in the mulitfractal phase. We utilize the
Loschmidt echo dynamics by choosing different eigenstates as initial states and
sudden changing the parameters of the system to distinguish the phases in the
presence of such system.
