  D0-branes on a D2-brane with a constant background B-field are unstable due
to the presence of a tachyonic mode and expected to dissolve into the D2-brane
to formulate a constant D0-charge density. In this paper we study such a
dissolution process in terms of a noncommutative gauge theory. Our results show
that the localized D0-brane spreads out over all of space on the D2-brane as
the tachyon rolls down into a stable vacuum. D0-branes on a D2-brane can be
described as unstable solitons in a noncommutative gauge theory in 2+1
dimensions in the Seiberg-Witten limit. In contrast to the case of annihilation
of a non-BPS D-brane, we are free from difficulty of disappearance of DOF,
since there exist open strings after the tachyon condensation. We solve an
equation of motion of the gauge field numerically, and our results show that
the localized soliton smears over all of noncommutative space. In addition, we
evaluate distributions of D-brane charge, F-string charge, and energy density
via formulas derived in Matrix theory. Our results show that the initial
singularities of D0-charge and energy density are resolved by turning on the
tachyon, and they disperse over the whole space on the D2-brane during the
tachyon condensation process.
