Dynamics of the molecular geometric phase

TL;DR

This paper explores the behavior of the molecular geometric phase during exact molecular dynamics, revealing how electron-nuclear interactions influence phase evolution and challenging the notion of its topological invariance.

Contribution

It introduces a gauge-invariant, dynamical phase definition using quantum hydrodynamics and demonstrates its evolution obeys a Maxwell-Faraday law, linking phase changes to non-conservative forces.

Findings

The phase evolution follows a Maxwell-Faraday induction law.

Non-conservative forces from electron dynamics can alter the phase.

Adiabatic conditions keep phase changes negligible.

Abstract

The fate of the molecular geometric phase in an exact dynamical framework is investigated with the help of the exact factorization of the wavefunction and a recently proposed quantum hydrodynamical description of its dynamics. An instantaneous, gauge invariant phase is introduced for arbitrary paths in nuclear configuration space in terms of hydrodynamical variables, and shown to reduce to the adiabatic geometric phase when the state is adiabatic and the path is closed. The evolution of the closed-path phase over time is shown to adhere to a Maxwell-Faraday induction law, with non-conservative forces arising from the electron dynamics that play the role of electromotive forces. We identify the pivotal forces that are able to change the value of the phase, thereby challenging any topological argument. Nonetheless, negligible changes in the phase occur when the local dynamics along the probe loop is approximately adiabatic. In other words, the adiabatic idealization of geometric phase effects may remain suitable for effectively describing certain dynamic observables.