Published March 17, 2022 | Version v1
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Energy, Momentum, and Angular Momentum Transfer between Electrons and Nuclei

  • 1. Max Planck Institute of Microstructure Physics, Halle (Saale), Germany; Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel; Beijing National Laboratory for Molecular Sciences, College ofChemistry and Molecular Engineering, Peking University, People's Republic of China
  • 2. Max Planck Institute of Microstructure Physics, Halle (Saale), Germany; Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

Description

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 Schrödinger 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.

Notes

Research funded by European Research Council Advanced Grant FACT (ERC-2017-AdG-788890).

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Funding

European Commission
FACT – Factorizing the wave function of large quantum systems 788890