Quantum points/patterns, Part 2: from quantum points to quantum patterns via multiresolution

Antonina N. Fedorova; Michael G. Zeitlin

doi:10.1117/12.893537

28 September 2011 Quantum points/patterns, Part 2: from quantum points to quantum patterns via multiresolution

Antonina N. Fedorova, Michael G. Zeitlin

Proceedings Volume 8121, The Nature of Light: What are Photons? IV; 81210K (2011) https://doi.org/10.1117/12.893537
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

It is obvious that we still have not any unified framework covering a zoo of interpretations of Quantum Mechanics, as well as satisfactory understanding of main ingredients of a phenomena like entanglement. The starting point is an idea to describe properly the key ingredient of the area, namely point/particle-like objects (physical quantum points/particles or, at least, structureless but quantum objects) and to change point (wave) functions by sheaves to the sheaf wave functions (Quantum Sheaves). In such an approach Quantum States are sections of the coherent sheaves or contravariant functors from the kinematical category describing space-time to other one, Quantum Dynamical Category, properly describing the complex dynamics of Quantum Patterns. The objects of this category are some filtrations on the functional realization of Hilbert space of Quantum States. In this Part 2, the sequel of Part 1, we present a family of methods which can describe important details of complex behaviour in quantum ensembles: the creation of nontrivial patterns, localized, chaotic, entangled or decoherent, from the fundamental basic localized (nonlinear) eigenmodes (in contrast with orthodox gaussian-like) in various collective models arising from the quantum hierarchies described by Wigner-like equations.

Citation Download Citation

Antonina N. Fedorova and Michael G. Zeitlin "Quantum points/patterns, Part 2: from quantum points to quantum patterns via multiresolution", Proc. SPIE 8121, The Nature of Light: What are Photons? IV, 81210K (28 September 2011); https://doi.org/10.1117/12.893537

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available