Quantum Kerr oscillators' evolution in phase space: Wigner current, symmetries, shear suppression and special states

The creation of quantum coherences requires a system to be anharmonic. The simplest such continuous one-dimensional quantum system is the Kerr oscillator. It has a number of interesting symmetries we derive. Its quantum dynamics is best studied in phase space, using Wigner's distribution W and the associated Wigner phase space current J. Expressions for the continuity equation governing its time evolution are derived in terms of J and it is shown that J for Kerr oscillators follows circles in phase space. Using J we also show that the evolution's classical shear in phase space is quantum suppressed by an effective "viscosity." Quantifying this shear suppression provides measures to contrast classical with quantum evolution and allows us to identify special quantum states.