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arXiv:quant-ph/0003103 · Physics Letters A

Effectively classical quantum states for open systems

Ph. Blanchard, Robert Olkiewicz

Published Aug 1, 2000• 10 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(00)00507-7

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We present a general formalism for studying the effects of dynamical heterogeneity in opens quantum systems. We develop this formalism in the state-space of density operators, on which ensembles of quantum states can be conveniently represented by probability distributions. We describe how this representation reduces ambiguity in the definition of quantum ensembles by providing the ability to explicitly separate classical and quantum sources of probabilistic uncertainty. We then derive explicit equations of motion for state-space distributions of both open and closed quantum systems and demonstrate that resulting dynamics take a fluid mechanical form analogous to a classical probability fluid on Hamiltonian phase-space, thus enabling a straightforward quantum generalization of Liouville's theorem. We illustrate the utility of our formalism by analyzing the dynamics of an open two-level system using the state-space formalism that are shown to be consistent with the derived analytical results.