Localization and pattern formation in quantum physics: I. Phenomena of localization

Antonina N. Fedorova; Michael G. Zeitlin

doi:10.1117/12.624110

4 August 2005 Localization and pattern formation in quantum physics: I. Phenomena of localization

Antonina N. Fedorova, Michael G. Zeitlin

Proceedings Volume 5866, The Nature of Light: What Is a Photon?; (2005) https://doi.org/10.1117/12.624110
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems, e.g., where the standard "coherent-states" approach cannot be applied. The key points demonstrating advantages of this approach are: (i) effects of localization of possible quantum states, more proper than "gaussian-like states"; (ii) effects of non-perturbative multiscales which cannot be calculated by means of perturbation approaches; (iii) effects of formation of complex quantum patterns from localized modes or classification and possible control of the full zoo of quantum states, including (meta) stable localized patterns (waveletons). In this first part we consider the applications of numerical-analytical technique based on local nonlinear harmonic analysis to quantum/quasiclassical description of nonlinear (polynomial/rational) dynamical problems which appear in many areas of physics. We'll consider calculations of Wigner functions as the solution of Wigner-Moyal-von Neumann equation(s) corresponding to polynomial Hamiltonians. Modeling demonstrates the appearance of (meta) stable patterns generated by high-localized (coherent) structures or entangled/chaotic behaviour. We can control the type of behaviour on the level of reduced algebraical variational system. At the end we presented the qualitative definition of the Quantum Objects in comparison with their Classical Counterparts, which natural domain of definition is the category of multiscale/multiresolution decompositions according to the action of internal/hidden symmetry of the proper realization of scales of functional spaces (the multiscale decompositions of the scales of Hilbert spaces of states). It gives rational natural explanation of such pure quantum effects as "self-interaction" (self-interference) and instantaneous quantum interaction (transmission of information).

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Antonina N. Fedorova and Michael G. Zeitlin "Localization and pattern formation in quantum physics: I. Phenomena of localization", Proc. SPIE 5866, The Nature of Light: What Is a Photon?, (4 August 2005); https://doi.org/10.1117/12.624110

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