• diffusive current;
  • the Hall effect

The master equation approach to diffusive current of bosonic or fermionic carriers in one- and two-dimensional lattices is discussed. This approach is shown to reproduce all known results of the linear response theory, including the integer quantum Hall effect for fermionic carriers. The main advantage of the approach is that it allows to calculate the current beyond the linear response regime where new effects are found. In particular, the Hall current can be inverted by changing orientation of the static force (electric field) relative to the primary axes of the lattice.