Fluid models of mixed quantum-classical dynamics

DOI10.1007/S00332-024-10044-4arXiv2306.15652MaRDI QIDQ6441717

Publication date: 27 June 2023

Abstract: Several efforts 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. As the quantum potential in Madelung hydrodynamics leads to severe challenges, one often seeks to neglect its contribution thereby approximating nuclear motion as classical. Then, the resulting model couples classical hydrodynamics for the nuclei to the quantum motion of the electronic component. Such 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 second-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 new quantum-classical fluid system that resolves these issues. 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, thereby inheriting variational and Hamiltonian structures, and ensuring energy/momentum balance. After discussing some of its structural properties and dynamical invariants, we illustrate the proposed fluid model in the case of pure-dephasing systems. We conclude with a presentation of some invariant planar models.

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