  Electrons in tight-binding lattice driven by DC electric field dissipate
their energy through on-site fermionic thermostats. Due to the translational
invariance in the transport direction, the problem can be block-diagonalized.
We solve this time-dependent quadratic problem and demonstrate that the problem
has an oscillatory steady-state. The steady-state occupation number shows that
the Fermi surface disappears for any damping from the thermostats and any
finite electric field. Despite the lack of momentum scattering, the
conductivity takes the same form as the semi-classical Ohmic expression from
the relaxation-time approximation.
