  An exact Quantum Kinetic Monte Carlo method is proposed to calculate electron
transport for 1D Fermi Hubbard model. The method is directly formulated in real
time and can be applied to extract time dependent dynamics of general
interacting Fermion models in 1D. When coupled with Density Functional Theory
and Maximally Localized Wannier Functions, our method can be used to predict
electron transport in materials in presence of interfaces. The first
application of our method on case study of $\alpha$-quartz dielectric breakdown
seems promising.
