Exact Quantum-Statistical Dynamics of Time-Dependent Generalized   Oscillators
  Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the thermal Wigner function about a classical trajectory in phase space. The contour of the Wigner function depicts an elliptical orbit with a constant area moving about the classical trajectory, whose eccentricity determines the squeezing of the initial vacuum. 
Sang Pyo Kim (Kunsan Nat'l Univ.) and Don N. Page (Univ. Alberta)