15th Experimental Chaos and Complexity Conference, Madrid, June 4-7, 2018 - "Complex Quantum World on the Tower of Scales", P18
- "From Order to Disorder in Ensembles: Back and Forth. Localization and Pattern Formation in Hierarchies", P19
Abstracts: " Quantum World on the Tower of Scales" Oral paper Antonina N. Fedorova, Michael G. Zeitlin.
We present a family of methods which can describe complex behaviour in
quantum ensembles.
We demonstrate the creation of nontrivial (meta) stable states (patterns),
localized, chaotic, entangled or decoherent, from the basic localized
modes in various collective models arising from the quantum hierarchy described
by Wigner-like equations.
The advantages of such an approach are as follows:
"From Order to Disorder in Ensembles: Back and Forth. Localization and Pattern Formation in Hierarchies" We present universal framework for generation, analysis and control of non-trivial states/patterns in the complex systems like kinetic hierarchies describing general set-up for non-equilibrium dynamics and their important reductions. We start from the proper underlying functional spaces and their internal hidden symmetries which generate all dynamical effects. The key ingredients are orbits of these symmetries, their representations, and Local Nonlinear Harmonic Analysis on these orbits. All that provides the possibility to consider the maximally localized fundamental generic modes, non-linear (in case of the non-abelian underlying symmetRy) and non-gaussian, which are not so smooth as gaussians and as a consequence allowing to consider fractal-like images and possible scenarios for generation chaotic/stochastic dynamics on the level of representation theory. As a generic example we consider the modeling of fusion dynamics in plasma physics. |