15th Experimental Chaos and Complexity Conference, Madrid, June 4-7, 2018
  1. "Complex Quantum World on the Tower of Scales", P18
  2. "From Order to Disorder in Ensembles: Back and Forth. Localization and Pattern Formation in Hierarchies", P19

" 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:
i). the natural realization of localized states in any proper functional realization of (Hilbert) space of states,
ii). the representation of hidden symmetry of a chosen realization of the functional model describes the (whole) spectrum of possible states via the so-called multiresolution decomposition.
Effects we are interested in are as follows:
1. a hierarchy of internal/hidden scales (time, space, phase space);
2. non-perturbative multiscales: from slow to fast contributions, from the coarser to the finer level of resolution/decomposition;
3. the coexistence of the levels of hierarchy of multiscale dynamics with transitions between scales;
4. the realization of the key features of the complex quantum world such as the existence of chaotic and/or entangled states with possible destruction in "open/dissipative" regimes due to interactions with quantum/classical environment and transition to decoherent states.
The numerical simulation demonstrates the formation of various (meta) stable patterns or orbits generated by internal hidden symmetry from generic high-localized fundamental modes. In addition, we can control the type of behaviour on the pure algebraic level by means of properly reduced algebraic systems (generalized dispersion relations).

"From Order to Disorder in Ensembles: Back and Forth. Localization and Pattern Formation in Hierarchies"
Oral paper
Michael G. Zeitlin, Antonina N. Fedorova.

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.