No. 29 (00111) Family name : Zeitlin Given name : Michael Affiliation : Mathematical Methods in Mechanics Group, Institute of Problems of Mechanical Engineering, Russian Academy of Sciences Abbreviation : IPME RAS E-mail address : zeitlin@math.ipme.ru Title : NONTRIVIAL QUANTUM PATTERNS: ZOO OF THE SOLUTIONS OF WIGNER-MOYAL EQUATIONS Authors : Antonina N. Fedorova, Michael G. Zeitlin Abstract : We present the application of the variational-multiresolution analysis to the calculations of the solutions of Wigner/von Neumann/Moyal equations corresponding to the quantization of classical polynomial dynamical problems. Wigner-Weyl (symbols) framework, the multiresolution representations, the variational approach and the polynomial tensor algebra in Fock-like spaces are the key points. We construct the solutions via the complete multiscale expansions in the generalized coherent states (non-gaussians) or high-localized nonlinear eigenmodes in the base of the compactly supported wavelets and the wavelet packets. We demonstrate the appearance of zoo of (stable) localized patterns (waveletons). Quantum-classical correspondence is considered. As applications we consider decoherence, entanglement and non-gaussian part of SPS/RHIC/LHC physics.