  We study real-time dynamics of a charge carrier introduced into undoped Mott
insulator propagating under a constant electric field F on the t-J ladder and
square lattice. We calculate quasistationary current. In both systems adiabatic
regime is observed followed by the positive differential resistivity (PDR) at
moderate fields where carrier mobility is determined. Quantitative differences
between ladder and 2-dimensional (2D) system emerge when at large fields both
systems enter negative differential resistivity (NDR) regime. In the ladder
system Bloch-like oscillations prevail, while in 2D the current remains finite,
proportional to 1/F. The crossover between PDR and NDR regime in 2D is
accompanied by a change of the spatial structure of the propagating spin
polaron.
