General linear dynamics - quantum, classical or hybrid

Details General linear dynamics - quantum, classical or hybrid General linear dynamics - quantum, classical or hybrid

2011-03-18

arxiv.org/abs/1103.3589v1

J.Phys.Conf.Ser. 306 (2011) 012010

Physics

Quantum Physics

17 pages; based on invited talks at the conferences DICE2010 (Castiglioncello, Italia, Sept 13-17, 2010) and Quantum Field The

Scientific paper

10.1088/1742-6596/306/1/012010

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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