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Mathematical Physics
Title: Lagrangian trajectories and closure models in mixed quantum-classical dynamics
(Submitted on 3 Mar 2023 (v1), last revised 11 May 2023 (this version, v3))
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.
Submission history
From: Cesare Tronci [view email][v1] Fri, 3 Mar 2023 18:55:15 GMT (22kb)
[v2] Sat, 29 Apr 2023 00:37:15 GMT (22kb)
[v3] Thu, 11 May 2023 11:20:40 GMT (24kb)
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