Quantum Fractals

Author: Arkadiusz Jadczyk
Publisher: World Scientific
ISBN: 9814569887
Size: 48.83 MB
Format: PDF, ePub
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Quantum Fractals from the Author: Arkadiusz Jadczyk. Starting with numerical algorithms resulting in new kinds of amazing fractal patterns on the sphere, this book describes the theory underlying these phenomena and indicates possible future applications. The book also explores the following questions: What are fractals?How do fractal patterns emerge from quantum observations and relativistic light aberration effects?What are the open problems with iterated function systems based on Mobius transformations?Can quantum fractals be experimentally detected?What are quantum jumps?Is quantum theory complete and/or universal?Is the standard interpretation of Heisenberg's uncertainty relations accurate?What is Event Enhanced Quantum Theory and how does it differ from spontaneous localization theories?What are the possible applications of quantum fractals? Contents:IntroductionWhat are Quantum Fractals?:Cantor SetIterated Function SystemsCantor Set Through Matrix EigenvectorQuantum Iterated Function SystemsExample: The "Impossible" Quantum FractalAction on the PlaneLorentz Group, SL(2,ℂ), and Relativistic AberrationExamples:Hyperbolic Quantum FractalsControlling Chaotic Behavior and Fractal DimensionQuantum Fractals on n-SpheresAlgorithms for Generating Hyperbolic Quantum FractalsFoundational Questions:Stochastic Nature of Quantum Measurement ProcessesAre There Quantum Jumps?Bohmian MechanicsEvent Enhanced Quantum TheoryGhirardi–Rimini–Weber Spontaneous LocalizationHeisenberg's Uncertainty Principle and Quantum FractalsAre Quantum Fractals Real?Appendix A. Mathematical Concepts:Metric SpacesNormed SpacesMeasure and IntegralMarkov, Frobenius-Perron and Koopman OperatorsAppendix B. Minkowski Space Generalization of Euler-Rodrigues Formula:Alternative Derivation via SL(2,ℂ) Readership: Advanced undergraduate students and professionals in quantum chaos, as well as philosophers of science. Keywords:Fractals;Quantum Theory;Measurement;Uncertainty;Quantum Jumps;Mobius Transformations;IFS;Spin;Lorentz Group;Relativity;Aberration;Time;GRW;EEQT

A Trajectory Description Of Quantum Processes Ii Applications

Author: Ángel S. Sanz
Publisher: Springer
ISBN: 3642179746
Size: 56.78 MB
Format: PDF
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A Trajectory Description Of Quantum Processes Ii Applications from the Author: Ángel S. Sanz. Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning as an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This second volume is focussed on simple and basic applications of quantum processes such as interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering problems. The corresponding analysis is carried out within the Bohmian framework. By stressing its interpretational aspects, the book leads the reader to an alternative and complementary way to better understand the underlying quantum dynamics.

Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii

Author: David Carfi
Publisher: American Mathematical Soc.
ISBN: 0821891480
Size: 56.61 MB
Format: PDF
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Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii from the Author: David Carfi. This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.

Quantum Interaction

Author: Jerome R. Busemeyer
Publisher: Springer
ISBN: 3642356591
Size: 69.84 MB
Format: PDF
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Quantum Interaction from the Author: Jerome R. Busemeyer. This book constitutes the refereed proceedings of the 6th International Symposium on Quantum Interaction, QI 2012, held in Paris in June 2012. The 21 revised full papers presented were carefully reviewed and selected from 32 submissions. The papers cover various topics on quantum interaction.

Applying Fractals In Astronomy

Author: Andre HECK
Publisher: Springer Science & Business Media
ISBN: 3540543538
Size: 53.24 MB
Format: PDF, Mobi
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Applying Fractals In Astronomy from the Author: Andre HECK. 'Fractal geometry addressesitselfto questions that many people have been asking themselves. It con cerns an aspect of Nature that almost everybody had been conscious of, but could not address in a formal fashion. ' 'Fractal geometry seems to be the proper language to describe the complezity of many very compli cated shapes around us. ' (Mandelbrot, 1990a) 'I believe that fractals respond to a profound un easiness in man. ' (Mandelbrot, 1990b) The catchword fractal, ever since it was coined by Mandelbrot (1975) to refer to a class of abstract mathematical objects that were already known at the turn ofthe 19th century, has found an unprecedented resonance both inside and outside the scientific community. Fractal concepts, far more than the concepts of catastrophe theory introduced a few years earlier, are currently being applied not only in the physical sciences, but also in biology and medicine (Goldberger and West 1987). In the mid-eighties, Kadanoff (1986) asked the question: 'Why all the fuss about /ractals'! '. He offered a twofold answer: in the first place, it is 'because of the practical, technological importance of fractal objects'. Indeed he emphasised the relevance of these structures for materials scientists and oil drilling engineers, in search of structures with novel properties, or models for the flow of oil through the soil. His second answer was: 'Because of the intellectual interest of fractals '.

Fractal Time

Author: Susie Vrobel
Publisher: World Scientific
ISBN: 9814295973
Size: 68.90 MB
Format: PDF, ePub, Docs
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Fractal Time from the Author: Susie Vrobel. This book provides an interdisciplinary introduction to the notion of fractal time, starting from scratch with a philosophical and perceptual puzzle. How subjective duration varies, depending on the way we embed current content into contexts, is explained. The complexity of our temporal perspective depends on the number of nestings performed, i.e. on the number of contexts taken into account. This temporal contextualization is described against the background of the notion of fractal time. Our temporal interface, the Now, is portrayed as a fractal structure which arises from the distribution of content and contexts in two dimensions: the length and the depth of time. The leitmotif of the book is the notion of simultaneity, which determines the temporal structure of our interfaces. Recent research results are described which present and discuss a number of distorted temporal perspectives. It is suggested that dynamical diseases arise from unsuccessful nesting attempts, i.e. from failed contextualization. Successful nesting, by contrast, manifests itself in a "win-win handshake" between the observer-participant and his chosen context. The answer as to why a watched kettle never boils has repercussions in many a discipline. It would be of immense interest to anyone who works in the fields of cognitive and complexity sciences, psychology and the neurosciences, social medicine, philosophy and the arts.

Quantum Mechanics Diffusion And Chaotic Fractals

Author: Mohammed S. El Naschie
ISBN: 9780080420271
Size: 70.57 MB
Format: PDF
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Quantum Mechanics Diffusion And Chaotic Fractals from the Author: Mohammed S. El Naschie. The philosophical and analytical silhouette of quantum mechanics can only take shape against a background of classical mechanics. As classical mechanics has undergone a radical reappraisal with the discovery of deterministic chaos and fractals, then quantum mechanics must be looked at again from the viewpoint of nonlinear dynamics. This book does just that, not solely from the point of view of quantum chaos, but also by looking at the hidden chaotic roots of quantum mechanics. Several of the contributions included in the book are concerned with the geometrization of physics and its consequences for quantum mechanics. Besides the main theme of the book, other equally interesting interpretations are represented, including the cellular automaton version of quantum mechanics and a radical endophysical interpretation: another contribution looks at the possibility of chaos in Einstein's fundamental equations. Some of the papers presented here are destined to be the subject of debate, agreement and passionate disagreement for some time.

Quantum Graphs And Their Applications

Author: Gregory Berkolaiko
Publisher: American Mathematical Soc.
ISBN: 0821837656
Size: 61.49 MB
Format: PDF, ePub, Docs
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Quantum Graphs And Their Applications from the Author: Gregory Berkolaiko. This volume is a collection of articles dedicated to quantum graphs, a newly emerging interdisciplinary field related to various areas of mathematics and physics. The reader can find a broad overview of the theory of quantum graphs. The articles present methods coming from different areas of mathematics: number theory, combinatorics, mathematical physics, differential equations, spectral theory, global analysis, and theory of fractals. They also address various important applications, such as Anderson localization, electrical networks, quantum chaos, mesoscopic physics, superconductivity, optics, and biological modeling.

Fractals Of Brain Fractals Of Mind

Author: Earl R. Mac Cormac
Publisher: John Benjamins Publishing
ISBN: 9789027251275
Size: 38.86 MB
Format: PDF
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Fractals Of Brain Fractals Of Mind from the Author: Earl R. Mac Cormac. This collective volume is the first to discuss systematically what are the possibilities to model different aspects of brain and mind functioning with the formal means of fractal geometry and deterministic chaos. At stake here is not an approximation to the way of actual performance, but the possibility of brain and mind to implement nonlinear dynamic patterns in their functioning. The contributions discuss the following topics (among others): the edge-of- chaos dynamics in recursively organized neural systems and in intersensory interaction, the fractal timing of the neural functioning on different scales of brain networking, aspects of fractal neurodynamics and quantum chaos in novel biophysics, the fractal maximum-power evolution of brain and mind, the chaotic dynamics in the development of consciousness, etc. It is suggested that the margins of our capacity for phenomenal experience, are fractal-limit phenomena . Here the possibilities to prove the plausibility of fractal modeling with appropriate experimentation and rational reconstruction are also discussed. A conjecture is made that the brain vs. mind differentiation becomes possible, most probably, only with the imposition of appropriate symmetry groups implementing a flowing interface of features of local vs. global brain dynamics. (Series B)

International Workshop On Quantum Optics 2003

Author: Vitaliĭ Vladimirovich Samart︠s︡ev
Publisher: Society of Photo Optical
ISBN: 9780819453259
Size: 39.45 MB
Format: PDF, Kindle
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International Workshop On Quantum Optics 2003 from the Author: Vitaliĭ Vladimirovich Samart︠s︡ev. Proceedings of SPIE present the original research papers presented at SPIE conferences and other high-quality conferences in the broad-ranging fields of optics and photonics. These books provide prompt access to the latest innovations in research and technology in their respective fields. Proceedings of SPIE are among the most cited references in patent literature.