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        Wigner's quantum phase space current in weakly anharmonic weakly excited two-state systems

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        Author
        Kakofengitis, Dimitris
        Steuernagel, Ole
        Attention
        2299/19810
        Abstract
        There are no phase-space trajectories for anharmonic quantum systems, but Wigner’s phase-space representation of quantum mechanics features Wigner current J . This current reveals fine details of quantum dynamics – finer than is ordinarily thought accessible according to quantum folklore invoking Heisenberg’s uncertainty principle. Here, we focus on the simplest, most intuitive, and analytically accessible aspects of J . We investigate features of J for bound states of time-reversible, weakly-anharmonic one-dimensional quantum-mechanical systems which are weakly-excited. We establish that weakly-anharmonic potentials can be grouped into three distinct classes: hard, soft, and odd potentials. We stress connections between each other and the harmonic case. We show that their Wigner current fieldline patterns can be characterised by J ’s discrete stagnation points, how these arise and how a quantum system’s dynamics is constrained by the stagnation points’ topological charge conservation. We additionally show that quantum dynamics in phase space, in the case of vanishing Planck constant ̄ h or vanishing anharmonicity, does not pointwise converge to classical dynamics.
        Publication date
        2017-09-30
        Published in
        European Physical Journal Plus
        Published version
        https://doi.org/10.1140/epjp/i2017-11634-2
        Other links
        http://hdl.handle.net/2299/19810
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