  Novel physics arises when strongly correlated system is driven out of
equilibrium by external fields. Dramatic changes in physical properties, such
as conductivity, are empirically observed in strongly correlated materials
under high electric field. In particular, electric-field driven metal-insulator
transitions are well-known as the resistive switching effect in a variety of
materials, such as VO$_2$, V$_2$O$_3$ and other transition metal oxides. To
satisfactorily explain both the phenomenology and its underlying mechanism, it
is required to model microscopically the out-of-equilibrium dissipative lattice
system of interacting electrons. In this thesis, we developed a systematic
method of modeling non-equilibrium steady states for dissipative lattice
systems by means of Non-equilibrium Green's function and Dynamical Mean Field
Theory. We firstly establish a "minimum model" to formulate the strong-field
transport in non-interacting dissipative electron lattice. This model is
exactly soluble and convenient for discussing energy dissipation and
steady-state properties. The formalism is then combined with Dynamical Mean
Field Theory to provide a systematic framework describing the nonequilibrium
steady-state of correlated materials. We use the formalism to study the
strong-field transport properties of correlated materials, Mott insulators and
Dirac electrons in graphene. We concentrate on the microscopic description of
resistive switching. Of particular interest is the filament formation during
the dynamical phase transition, which has been interpreted as a result of the
delicate interplay between dissipation and Mott physics. We will also examine
$IV$ characteristics and particularly the current saturation of Dirac electrons
in graphene. The arXiv version has been updated with minor modifications and
corrections.
