Application of a semiclassical model for the second-quantized   many-electron Hamiltonian to nonequilibrium quantum transport: The resonant   level model
  A semiclassical (SC) approach is developed for nonequilibrium quantum transport in molecular junctions. Following the early work of Miller and White [J. Chem. Phys. 84, 5059 (1986)], the many-electron Hamiltonian in second quantization is mapped onto a classical model that preserves the fermionic character of electrons. The resulting classical electronic Hamiltonian allows for real-time molecular dynamics simulations of the many-body problem from an uncorrelated initial state to the steady state. Comparisons with exact results generated for the resonant level model reveal that a semiclassical treatment of transport provides a quantitative description of the dynamics at all relevant timescales for a wide range of bias and gate potentials, and for different temperatures. The approach opens a door to treating nontrivial quantum transport problems that remain far from the reach of fully quantum methodologies. 
David W.H. Swenson, Tal Levy, Guy Cohen, Eran Rabani, and William H.   Miller
cond-mat.mes-hall cond-mat.other quant-ph