Pattern Formation in Wigner-like Equations via Multiresolution

Abstract

We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points. We construct the solutions via the multiscale expansions in the generalized coherent states or high-localized nonlinear eigenmodes in the base of the compactly supported wavelets and the wavelet packets. We demonstrate the appearance of (stable) localized patterns (waveletons) and consider entanglement and decoherence as possible applications.

15 pages, 6 figures, ws-procs9x6.cls, Presented at Joint 28th ICFA Advanced Beam Dynamics & Advanced & Novel Accelerators Workshop on Quantum Aspects of Beam Physics and Other Critical Issues of Beams in Physics and Astrophysics, January 7-11, 2003, Hiroshima University, Higashi-Hiroshima, Japan

Cited by in corpus (4)

• Localization and Fusion Modeling in Plasma Physics. Part I: Math Framework for Non-Equilibrium Hierarchies
• Quantum points/patterns, Part 2. From quantum points to quantum patterns via multiresolution
• Quantum points/patterns, Part 1. From geometrical points to quantum points in a sheaf framework
• Localization and Fusion Modeling in Plasma Physics. Part II: Vlasov-like Systems. Important Reductions