Complex fluid models of mixed quantum-classical dynamics
arXiv:2306.15652 · doi:10.1007/s00332-024-10044-4
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.
arXiv comment29 pages. No figures. To appear in J. Nonlinear Sci
References in corpus (21)
- Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
- Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction
- Motion of vortex lines in quantum mechanics
- Spin and charge pumping by steady or pulse current-driven magnetic domain wall: A self-consistent multiscale time-dependent-quantum/time-dependent-classical approach
- Koopman wavefunctions and classical-quantum correlation dynamics
- Hybrid Quantum-Classical Master Equations
- Bohmian mechanics in the exact factorization of electron-nuclear wavefunction
- Madelung transform and probability densities in hybrid classical-quantum dynamics
- Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation
- A Phase-Space Semiclassical Approach for Modeling Nonadiabatic Nuclear Dynamics with Electronic Spin
- Phase space methods for the spin dynamics in condensed matter systems
- Evolution of hybrid quantum-classical wavefunctions
- Geometry of nonadiabatic quantum hydrodynamics
- Canonical description of cosmological backreaction
- Hybrid quantum-classical dynamics of pure-dephasing systems
- The bohmion method in nonadiabatic quantum hydrodynamics
- Energy-Casimir stability of hybrid Vlasov-MHD models
- Overcoming positivity violations for density matrices in surface hopping
- An Efficient Time-splitting Method for the Ehrenfest Dynamics
- Lagrangian trajectories and closure models in mixed quantum-classical dynamics
- Hybrid models for complex fluids with multipolar interactions