# The Wigner Current for Open Quantum Systems

## TL;DR

This paper extends the Wigner current framework to open quantum systems, providing a geometric phase space perspective on decoherence and stabilization mechanisms in bosonic modes interacting with environments.

## Contribution

It introduces a Wigner current formulation for open quantum systems and demonstrates its utility through examples involving harmonic and nonlinear oscillators.

## Key findings

- Wigner current offers geometric insights into decoherence processes.
- Nonlinearity can help stabilize quantum states against environmental effects.
- The approach applies to single bosonic mode systems interacting with an environment.

## Abstract

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).