Lagrangian trajectories and closure models in mixed quantum-classical dynamics

Abstract

Mixed quantum-classical models have been proposed in several contexts to overcome the computational challenges of fully quantum approaches. However, current models typically suffer from long-standing consistency issues, and, in some cases, invalidate Heisenberg's uncertainty principle. Here, we present a fully Hamiltonian theory of quantum-classical dynamics that appears to be the first to ensure a series of consistency properties, beyond positivity of quantum and classical densities. Based on Lagrangian phase-space paths, the model possesses a quantum-classical Poincaré integral invariant as well as infinite classes of Casimir functionals. We also exploit Lagrangian trajectories to formulate a finite-dimensional closure scheme for numerical implementations.

arXiv comment10 pages, no figure. To appear in Lecture Notes in Comput. Sci

References in corpus (4)

• Koopman wavefunctions and classical-quantum correlation dynamics
• Geometry of nonadiabatic quantum hydrodynamics
• Evolution of hybrid quantum-classical wavefunctions
• The bohmion method in nonadiabatic quantum hydrodynamics

Cited by in corpus (5)

• Complex fluid models of mixed quantum-classical dynamics
• Koopmon trajectories in nonadiabatic quantum-classical dynamics
• Heisenberg dynamics of mixed quantum-classical systems
• Madelung transform and variational asymptotics in Born-Oppenheimer molecular dynamics
• Separability and entanglement in classical eigenfunctions as a criterion for Hamiltonian chaos