Kinetic equations governing time evolution of positions and momenta of atoms in extended systems are derived using quantum-classical ensembles within the nonequilibrium statistical operator method (NESOM). Ions are treated classically, while their electrons quantum mechanically; however, the statistical operator is not factorized in any way and no simplifying assumptions are made concerning the electronic subsystem. Using this method, we derive kinetic equations of motion for the classical degrees of freedom (atoms) which account fully for the interaction and energy exchange with the quantum variables (electrons). Our equations, alongside the usual “Newton-like” terms normally associated with the Ehrenfest dynamics, contain additional terms, proportional to the atoms velocities, which can be associated with the “electronic friction.” Although previously electronic friction was introduced into molecular dynamics equations of atoms only using model treatments, we show that this result is general and model independent and thus must be expected in treating any system as an additional force acting on slow degrees of freedom due to coupling with the fast ones. Possible ways of calculating the friction forces, which are shown to be given via complicated nonequilibrium correlation functions, are discussed. In particular, we demonstrate that the correlation functions are directly related to the thermodynamic Matsubara Green’s functions, and this relationship allows for the diagrammatic methods to be used in treating electron-electron interaction perturbatively when calculating the correlation functions.

• Received 19 July 2007

DOI:https://doi.org/10.1103/PhysRevB.76.144304