Exact-factorization framework for electron-nuclear dynamics in electromagnetic fields

TL;DR

This paper extends the Exact Factorization framework to include electromagnetic fields, revealing the interplay between magnetic and Berry-curvature effects and proving a compensation property in non-adiabatic electron-nuclear dynamics.

Contribution

The authors generalize the EF formalism to systems under electromagnetic fields and rigorously prove the compensation between magnetic and Berry-curvature fields.

Findings

Revealed the interplay between magnetic and Berry-curvature fields in EF.

Proved the compensation property in non-adiabatic dynamics.

Extended EF theory to include electromagnetic interactions.

Abstract

The Exact Factorization (EF) theory aims at the separation of the nuclear and electronic degrees of freedom in the many-body (MB) quantum mechanical problem. Being formally equivalent to the solution of the MB Schr\"{o}dinger equation, EF sets up a strategy for the construction of efficient approximations in the theory of the correlated electronic-nuclear motion. Here we extend the EF formalism to incorporate the case of a system under the action of an electromagnetic field. An important interplay between the physical magnetic and the Berry-curvature fields is revealed and discussed within the fully non-adiabatic theory. In particular, it is a known property of the Born-Oppenheimer approximation that, for a neutral atom in a uniform magnetic field, the latter is compensated by the Berry-curvature field in the nuclear equation of motion (\citet{Yin-92}). From an intuitive argument that the atom must not be deflected by the Lorentz force from a straight line trajectory, it has been conjectured that the same compensation should occur within the EF theory as well. We give a rigorous proof of this property.