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arXiv:1306.4480 · Journal of Physics Conference Series

Quantum-classical hybrid dynamics – a summary

Hans-Thomas Elze

Published Jun 10, 2013• 17 citations
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Abstract

A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of classical Hamiltonian mechanics suitably extended to quantum mechanics.
DOI
10.1088/1742-6596/442/1/012007

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We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. This is of practical as well as of foundational interest and no fully satisfactory solution of this problem has been established to date. Related aspects will be observed in a general linear ensemble theory, which comprises classical and quantum dynamics in the form of Liouville and von Neumann equations, respectively, as special cases. Considering the simplest object characterized by a two-dimensional state-space, we illustrate how quantum mechanics is special in several respects among possible linear generalizations.
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Four questions are discussed which may be addressed to any proposal of a quantum-classical hybrid theory which concerns the direct coupling of classical and quantum mechanical degrees of freedom. In particular, we consider the formulation of hybrid dynamics presented recently in Ref. [1]. This linear theory differs from the nonlinear ensemble theory of Hall and Reginatto, but shares with it to fulfil all consistency requirements discussed in the literature, while earlier attempts failed. - Here, we additionally ask: Does the theory allow for superposition, separable, and entangled states originating in the quantum mechanical sector? Does it allow for "Free Will", as introduced, in this context, by Diósi [2]? Is it local? Does it provide hints for the emergence of quantum mechanics from dynamics beneath?