# Born-Oppenheimer Dynamics, Electronic Friction, and the Inclusion of Electron-Electron Interactions

## TL;DR

This paper derives a universal expression for electronic friction applicable to systems with electron-electron interactions, using a quantum-classical approach, and demonstrates its significance through the Anderson-Holstein model showing correlation effects like the Kondo resonance.

## Contribution

It introduces a general formula for electronic friction that includes electron-electron interactions, extending previous models that neglected correlations.

## Key findings

- The derived friction expression is fully general and reduces to known forms for non-interacting cases.
- Electron-electron interactions significantly influence electronic friction, as shown in the Anderson-Holstein model.
- Proper treatment of correlations reveals features like the Kondo resonance absent in mean-field approaches.

## Abstract

We present a universal expression for the electronic friction as felt by a set of classical nuclear degrees of freedom (DoF's) coupled to a manifold of quantum electronic DoF's; no assumptions are made regarding the nature of the electronic Hamiltonian and electron-electron repulsions are allowed. Our derivation is based on a quantum-classical Liouville equation (QCLE) for the coupled electronic-nuclear motion, followed by an adiabatic approximation whereby electronic transitions are assumed to equilibrate faster than nuclear movement. The resulting form of friction is completely general, but does reduce to previously published expressions for the quadratic Hamiltonian (i.e. Hamiltonians without electronic correlation). At equilibrium, the second fluctuation-dissipation theorem is satisfied and the frictional matrix is symmetric. To demonstrate the importance of electron-electron correlation, we study electronic friction within the Anderson-Holstein model, where a proper treatment of electron-electron interactions shows signatures of a Kondo resonance and a mean-field treatment is completely inadequate.