  We investigate the dust velocity and spatial distribution in an eccentric
protoplanetary disk under the secular gravitational perturbation of an embedded
planet of about 5 Jupiter masses. We first employ the FARGO code to obtain the
two-dimensional density and velocity profiles of the eccentric gas disk
exterior to the gap opened up by the embedded planet in the quasi-steady state.
We then apply the secular perturbation theory and incorporate the gas drag to
estimate the dust velocity and density on the secular timescale. The
dust-to-gas ratio of the unperturbed disk is simply assumed to be 0.01. In our
fiducial disk model with the planet at 5 AU, we find that 0.01 cm- to 1 m-sized
dust particles are well coupled to the gas. Consequently, the particles behave
similarly to the gas and exhibit asymmetric dynamics as a result of eccentric
orbits. The dust surface density is enhanced around the apocenter of the disk.
However, for the case of a low-density gaseous disk (termed "transition disk"
henceforth in this work) harboring the planet at 100 AU, the azimuthal
distributions of dust of various sizes can deviate significantly. Overall, the
asymmetric structure exhibits a phase correlation between the gas velocity
fields and dust density distribution. Therefore, our study potentially provides
a reality check as to whether an asymmetric disk gap detected at sub-millimeter
and centimeter wavelengths is a signpost of a massive gas giant planet.
