Energy, Momentum and Angular Momentum Transfer Between Electrons and Nuclei

TL;DR

This paper derives subsystem Ehrenfest identities within the exact factorization framework to quantify energy, momentum, and angular momentum transfer between electrons and nuclei, highlighting the role of effective electromagnetic fields and Berry curvature.

Contribution

It introduces new subsystem Ehrenfest identities based on the exact factorization approach, linking electromagnetic potentials and Berry curvature to energy and momentum transfer.

Findings

Effective electromagnetic force operators are derived for energy, momentum, and angular momentum transfer.

Berry curvature components are identified with classical and non-classical magnetic fields.

Two examples demonstrate the identities' usefulness in electron-phonon systems.

Abstract

The recently developed exact factorization approach condenses all electronic effects on the nuclear subsystem into scalar and vector potentials that appear in an effective time dependent Schr\"{o}dinger equation. Starting from this equation, we derive subsystem Ehrenfest identities characterizing the energy, momentum and angular momentum transfer between electrons and nuclei. An effective electromagnetic force operator induced by the electromagnetic field corresponding to the effective scalar and vector potentials appears in all three identities. The effective magnetic field has two components that can be identified with the Berry curvature calculated with (a) different cartesian coordinates of the same nucleus and (b) arbitrary cartesian coordinates of two different nuclei. (a) has a classical interpretation as the induced magnetic field felt by the nucleus, while (b) has no classical analog. Subsystem Ehrenfest identities are ideally suited for quantifying energy transfer in electron-phonon systems. With two explicit examples we demonstrate the usefulness of the new identities.