Energy, momentum and angular momentum are the unique variables that obey conservation laws and have the same meaning in classical and quantum mechanics. Their exchange between electrons and nuclei is crucial to understanding a variety of mechanisms, such as the fast internal conversion of DNA and RNA, the relaxation of hot electrons in solids, the electronic friction-induced relaxation of molecular vibrations, chemical dynamics including collision processes, combustions and explosions, quantum thermodynamics, etc. Knowledge of the mechanisms in these problems may facilitate the design of functional devices on the molecular scale, such as molecular motors and refrigerators, minimizing Joule heating in electronics, and reducing the rate of heat dissipation in solar cells and fluorescence processes.
In this paper, we extend the well-known Ehrenfest theorem that describes the rate of change of the expectation values of position and momentum of a one-component system to systems with multiple species. In particular, for systems composed of electrons and nuclei, we derive three inter-subsystem Ehrenfest identities giving the rate of change of the kinetic energy, momentum and angular momentum of the nuclei. Moreover, the same effective electromagnetic force operator appears in all three identities. The force includes the effects of an induced electromagnetic field corresponding to the effective scalar and vector potentials acting on the nuclei.
The effective magnetic field has two components that can be identified with the Berry curvature calculated with (i) different cartesian coordinates of the same nucleus and (ii) arbitrary cartesian coordinates of two different nuclei. (i) has a classical interpretation as the induced magnetic field felt by the nucleus, while (ii) has no classical analog. These magnetic fields along with the corresponding forces identified in this paper should aid in condensing the enormous amount of information in the electron-nuclear wave function into a few comprehensible quantities that help us better understand dynamical processes on the molecular scale.
This work was accomplished in collaboration with Dr. Ryan Requist and Prof. Hardy Gross.
For more details, please check the following link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.113001
