Lagrangian trajectories and closure models in mixed quantum-classical dynamics

• URL: http://arxiv.org/abs/2303.01975v3
• Date: Thu, 11 May 2023 11:20:40 GMT
• Title: Lagrangian trajectories and closure models in mixed quantum-classical dynamics
• Authors: Cesare Tronci, Fran\c{c}ois Gay-Balmaz
• Abstract summary: We present a fully Hamiltonian theory of quantum-classical dynamics that appears to be the first to ensure a series of consistency properties. Based on Lagrangian phase-space paths, the model possesses a quantum-classical Poincar'e integral invariant as well as infinite classes of Casimir functionals.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Poincar\'e 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.

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