  We perform an accurate time-dependent numerical study of out-of-equilibrium
response of a bound state within t-J systems on a two-leg ladder and a square
lattice. We show that the bound hole pair decays with the onset of finite
steady current if both mechanisms for binding and the dissipation share
matching degrees of freedom. Moreover, by investigating the mechanism of decay
on the square lattice we find that the dynamics is governed by the decay in the
direction perpendicular to the electric field, leading to much shorter decay
times in comparison to the ladder where such dynamics is topologically
restricted.
