TY - GEN
T1 - Lagrangian Trajectories and Closure Models in Mixed Quantum-Classical Dynamics
AU - Tronci, Cesare
AU - Gay-Balmaz, François
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - 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.
AB - 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.
KW - Hamilton’s variational principle
KW - Koopman wavefunction
KW - Lagrangian trajectory
KW - Mixed quantum-classical dynamics
KW - group action
U2 - 10.1007/978-3-031-38299-4_31
DO - 10.1007/978-3-031-38299-4_31
M3 - Conference contribution
AN - SCOPUS:85162789234
SN - 9783031382987
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 290
EP - 300
BT - Geometric Science of Information - 6th International Conference, GSI 2023, Proceedings
A2 - Nielsen, Frank
A2 - Barbaresco, Frédéric
PB - Springer Science and Business Media Deutschland GmbH
T2 - The 6th International Conference on Geometric Science of Information, GSI 2023
Y2 - 30 August 2023 through 1 September 2023
ER -