Dynamics of mixed quantum-classical spin systems

DOI10.1088/1751-8121/ACC145zbMATH Open1521.81084arXiv2210.00988MaRDI QIDQ6412743

Publication date: 3 October 2022

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.

Mathematics Subject Classification ID

Hamilton's equations (70H05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Spinor and twistor methods applied to problems in quantum theory (81R25) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Quantum measurement theory, state operations, state preparations (81P15) Lie bialgebras; Lie coalgebras (17B62) Extremal problems for conformal and quasiconformal mappings, variational methods (30C70) Nonholonomic systems related to the dynamics of a system of particles (70F25) Uncertainty relations, also entropic (81S07)

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