Localization and pattern formation in Wigner representation via   multiresolution
  We present an application of variational-wavelet analysis to quasiclassical calculations of solutions of Wigner equations related to nonlinear (polynomial) dynamical problems. (Naive) deformation quantization, multiresolution representations and variational approach are the key points. Numerical calculations demonstrates pattern formation from localized eigenmodes and transition from chaotic to localized (waveleton) types of behaviour. 
Antonina N. Fedorova, Michael G. Zeitlin