Pattern Formation in Wigner-like Equations via Multiresolution

Details Pattern Formation in Wigner-like Equations via Multiresolution Pattern Formation in Wigner-like Equations via Multiresolution

2003-06-29

arxiv.org/abs/quant-ph/0306197v1

Physics

Quantum Physics

15 pages, 6 figures, ws-procs9x6.cls, Presented at Joint 28th ICFA Advanced Beam Dynamics & Advanced & Novel Accelerators Work

Scientific paper

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.

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