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We extend the Wigner current vector field (Wigner current) construct tosingle bosonic mode quantum systems interacting with an environment. In termsof the Wigner function quasiprobability density and associated Wigner current,the open system quantum dynamics can be concisely expressed as a continuityequation. Through the consideration of the harmonic oscillator and additivelydriven Duffing oscillator in the bistable regime as illustrative systemexamples, we show how the evolving Wigner current vector field on the systemphase space yields useful geometric insights concerning how quantum statesdecohere away due to interactions with the environment, as well as how they maybe stabilized through the counteracting effects of the system anharmonicity(i.e., nonlinearity).

The Wigner Current for Open Quantum Systems