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We extend the Wigner current vector field (Wigner current) construct to single bosonic mode quantum systems interacting with an environment. In terms of the Wigner function quasiprobability density and associated Wigner current, the open system quantum dynamics can be concisely expressed as a continuity equation. Through the consideration of the harmonic oscillator and additively driven Duffing oscillator in the bistable regime as illustrative system examples, we show how the evolving Wigner current vector field on the system phase space yields useful geometric insights concerning how quantum states decohere away due to interactions with the environment, as well as how they may be stabilized through the counteracting effects of the system anharmonicity (i.e., nonlinearity).

In 1904 Bransford LewisJ reported the use of his operative cystoscope (Fig. 58), adapted not only to use within the bladder but also in the ureters. The direct-vision air cystoscopes of Luys, § and of CathelinU were submitted in 1904 and 1905, and attracted considerable attention in France. * We cannot agree with Fenwick who decries the necessity for a direct-view instrument, saying that by proper manipulation it is possible to obtain a satisfactory view of the posterior wall through the right-angle view cystoscope.

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The evolution of the discrete Wigner function is formally similar to a probabilistic process, but the transition probabilities, like the discrete Wigner function itself, can be negative. We investigate these transition probabilities, as well as the transition rates for a continuous process, aiming particularly to give simple criteria for deciding when a set of such quantities corresponds to a legitimate quantum process. We also show how the transition rates for any Hamiltonian evolution can be worked out by expanding the Hamiltonian as a linear combination of displacement operators in the discrete phase space.