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Nonequilibrium Molecular Dynamics Simulation of Interacting Many Electrons Scattered by Lattice Vibrations

We propose a new model suitable for a nonequilibrium molecular dynamics (MD) simulation of electrical conductors. The model consists of classical electrons and atoms. The atoms compose a lattice vibration system. The electrons are scattered by electron-electron and electron-atom interactions. Since the scattering cross section is physically more important than the functional form of a scattering potential, we propose to devise the electron-atom interaction potential in such a way that its scattering cross section agrees with that of quantum-mechanical one. To demonstrate advantages of the proposed model, we perform a nonequilibrium MD simulation assuming a doped semiconductor at room or higher temperature. In the linear response regime, we confirm Ohm's law, the dispersion relations and the fluctuation-dissipation relation. Furthermore, we obtain reasonable dependence of the electrical conductivity on temperature, despite the fact that our model is a classical model.