Evolution of Hybrid Quantum-Classical Wavefunctions

Gay–Balmaz, François; Tronci, Cesare

doi:10.2139/ssrn.4084947

Cited by 1 publication

(2 citation statements)

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“…Indeed, the characteristic nature of the equations (4) offers the possibility of devising trajectory methods, e.g. following [30,48,68]. However, the model ( 4)-( 6) involves the full classical phase-space, which makes the curse of dimensions particularly challenging.…”

Section: Quantum-classical Dynamics On Phase-spacementioning

confidence: 99%

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Dynamics of mixed quantum–classical spin systems ^*

Gay–Balmaz

Tronci

2023

J. Phys. A: Math. Theor.

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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.

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Section: Quantum-classical Dynamics On Phase-spacementioning

confidence: 99%

“…Within the context of mixed quantum-classical dynamics, a phasespace extension of the Mead connection made its first appearance in the original model ( 4)- (6). Indeed, as shown in [38,68], equation ( 5) may be rewritten as…”

Section: Mead Connection and The Stress Tensormentioning

confidence: 99%