Dynamics of mixed quantum-classical spin systems
arXiv:2210.00988 · doi:10.1088/1751-8121/acc145
Abstract
Mixed quantum-classical spin systems have been proposed in spin chain theory and, more recently, in magnon spintronics. However, current models of quantum-classical dynamics beyond mean-field approximations 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 spin dynamics that appears to be the first to ensure an entire series of consistency properties, including positivity of both the classical and the quantum density, so that Heisenberg's principle is satisfied at all times. We show how this theory may connect to recent energy-balance considerations in measurement theory and we present its Poisson bracket structure explicitly. After focusing on the simpler case of a classical Bloch vector interacting with a quantum spin observable, we illustrate the extension of the model to systems with several spins, and restore the presence of orbital degrees of freedom.
Submitted as a contribution to the Special Collection "Koopman methods in classical and quantum-classical mechanics" in the Journal of Physics A. Revised version
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- Koopmon trajectories in nonadiabatic quantum-classical dynamics
- Hybrid quantum-classical systems: statistics, entropy, microcanonical ensemble and its connection to the canonical ensemble
- Heisenberg dynamics of mixed quantum-classical systems
- Few-Photon Fluorescence from Ultracold Bosons in an Optical Cavity