Complex fluid models of mixed quantum-classical dynamics

TL;DR

This paper introduces a new complex fluid model for mixed quantum-classical dynamics that maintains a Hamiltonian structure and energy-momentum conservation, addressing previous mathematical and computational challenges.

Contribution

The authors develop a novel complex fluid system derived from the phase-space action principle, ensuring mathematical consistency and preserving key physical invariants.

Findings

The new model retains Hamiltonian structure and conservation laws.

It effectively describes pure-dephasing quantum dynamics.

Invariant planar models are also presented.

Abstract

Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential leads to severe computational challenges and one often seeks to neglect its contribution, thereby approximating nuclear motion as classical. The resulting model couples classical hydrodynamics for the nuclei to the quantum motion of the electronic component, leading to the structure of a complex fluid system. This type of mixed quantum-classical fluid models have also appeared in solvation dynamics to describe the coupling between liquid solvents and the quantum solute molecule. While these approaches represent a promising direction, their mathematical structure requires a certain care. In some cases, challenging higher-order gradients make these equations hardly tractable. In other cases, these models are based on phase-space formulations that suffer from well-known consistency issues. Here, we present a new complex fluid system that resolves these difficulties. Unlike common approaches, the current system is obtained by applying the fluid closure at the level of the action principle of the original phase-space model. As a result, the system inherits a Hamiltonian structure and retains energy/momentum balance. After discussing some of its structural properties and dynamical invariants, we illustrate the model in the case of pure-dephasing dynamics. We conclude by presenting some invariant planar models.