General linear dynamics - quantum, classical or hybrid

Abstract

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.

17 pages; based on invited talks at the conferences DICE2010 (Castiglioncello, Italia, Sept 13-17, 2010) and Quantum Field Theory and Gravity (Regensburg, Germany, Sept 28 - Oct 1, 2010)

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Cited by in corpus (8)

• Linear dynamics of quantum-classical hybrids
• Four questions for quantum-classical hybrid theory
• The Quantum as an Emergent System
• Proliferation of observables and measurement in quantum-classical hybrids
• Classical-Quantum Coexistence: a `Free Will' Test
• Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation
• Modeling double slit interference via anomalous diffusion: independently variable slit widths
• Hydrogen atom as a quantum-classical hybrid system