Non-equilibrium statistical mechanics of classical nuclei interacting with the quantum electron gas

TL;DR

This paper derives kinetic equations for classical nuclei interacting with a quantum electron gas using NESOM, revealing additional velocity-dependent friction terms and connecting correlation functions to Matsubara Green's functions, advancing non-equilibrium statistical mechanics.

Contribution

It introduces a comprehensive derivation of kinetic equations that include electronic friction without simplifying assumptions, linking correlation functions to Green's functions for perturbative calculations.

Findings

Derived kinetic equations with electronic friction terms.

Connected correlation functions to Matsubara Green's functions.

Provided a framework for perturbative treatment of electron-electron interactions.

Abstract

Kinetic equations governing time evolution of positions and momenta of atoms in extended systems are derived using quantum-classical ensembles within the Non-Equilibrium Statistical Operator Method (NESOM). Ions are treated classically, while their electrons quantum mechanically; however, the statistical operator is not factorised 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 Newtonian-like terms normally associated with the Ehrenfest dynamics, contain additional terms, proportional to the atoms velocities, which can be associated with the electronic friction. Possible ways of calculating the friction forces which are shown to be given via complicated non-equilibrium 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. This work also generalises previous attempts, mostly based on model systems, of introducing the electronic friction into Molecular Dynamics equations of atoms.