Correlated electron-phonon transport from molecular dynamics with   quantum baths
  Based on generalized quantum Langevin equations for the tight-binding wave function amplitudes and lattice displacements, electron and phonon quantum transport are obtained exactly using molecular dynamics (MD) in the ballistic regime. The electron-phonon interactions can be handled with a quasi-classical approximation. Both charge and energy transport and their interplay can be studied. We compare the MD results with that of a fully quantum mechanical nonequilibrium Green's function (NEGF) approach for the electron currents. We find a ballistic to diffusive transition of the electron conduction in one dimensional chains as the chain length increases. 
J. T. Lu and Jian-Sheng Wang