Berlin 2018 – scientific program
DY 50.10: Talk
Wednesday, March 14, 2018, 18:00–18:15, EB 107
Quantum Dynamics beyond Gaussians: from Coarse Graining to a Tower of Scales via Multiresolution — •Antonina N. Fedorova and Michael G. Zeitlin — Russia, 199178, St.Petersburg, V.O. Bolshoj pr., 61, IPME RAS, Mathematical Methods in Mechanics Group
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-Moyal-von Neumann-like equations. The advantages of such an approach are as follows: i). the natural description of localized states in any proper functional realization of (Hilbert) space of states, ii). the representation of hidden symmetry of a chosen representation of the functional model describes the (whole) spectrum of possible states via the 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 manifestation 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.