  We study the nonequilibrium steady state of a Mott insulator coupled to a
thermostat and driven by a constant electric field, starting from weak fields,
until the dielectric breakdown, and beyond. We find that the conventional Zener
picture does not describe the steady-state physics. In particular, the current
at weak field is found to be controlled by the dissipation. Moreover, in
connection with the electric-field-driven dimensional crossover, we find that
the dielectric breakdown occurs when the field strength is on the order of the
Mott gap of the corresponding lower-dimensional system. We also report a
resonance and the meltdown of the quasiparticle peak when the field strength is
half of this Mott gap.
