Floquet driven frictional effects

TL;DR

This paper develops a theoretical framework using Floquet theory to describe electronic friction and non-adiabatic effects in strongly driven electron-nuclear systems, revealing novel Lorentz-like forces.

Contribution

It derives a Floquet-based Fokker-Planck equation for non-adiabatic dynamics, including explicit electronic friction terms and their properties, advancing understanding of driven molecular systems.

Findings

Floquet electronic friction tensor has antisymmetric components at equilibrium.

Reveals Lorentz-like forces in Floquet driven non-Born Oppenheimer dynamics.

Provides a new derivation of Floquet quantum-classical Liouville equation.

Abstract

When the coupled electron-nuclear dynamics are subjected to strong Floquet driving, there is a strong breakdown of the Born-Oppenheimer approximation. In this article, we derive a Fokker-Planck equation to describe non-adiabatic molecular dynamics with electronic friction for Floquet driven systems. We first provide a new derivation of the Floquet quantum-classical Liouville equation (QCLE) for driven electron-nuclear dynamics. We then transform the Floquet QCLE into a Fokker-Planck equation with explicit forms of frictional force and random force. We recast the electronic friction in terms of Floquet Green's functions such that we can evaluate the electronic friction explicitly. We show that the Floquet electronic friction tensor exhibits antisymmetric terms even at equilibrium for real-valued Hamiltonian, suggesting that there is a Lorentz-like force in Floquet driven non-Born Oppenheimer dynamics even without any spin-orbit couplings.