Quantum Fractals

Author: Arkadiusz Jadczyk
Publisher: World Scientific
ISBN: 9814569887
Size: 61.60 MB
Format: PDF, Docs
View: 4668
Download Read Online

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: 37.47 MB
Format: PDF, Mobi
View: 2305
Download Read Online

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.

The Fractal Prince

Author: Hannu Rajaniemi
Publisher: Hachette UK
ISBN: 0575088958
Size: 60.14 MB
Format: PDF, ePub, Docs
View: 1224
Download Read Online

The Fractal Prince from the Author: Hannu Rajaniemi. Jean le Flambeur is out of prison, but still not free. To pay his debts he has to break into the mind of a living god. But when the stakes are revealed, Jean has to decide how far he is willing to go to get the job done. The sequel to Hannu Rajaniemi's extraordinary debut novel is set to build on the extravagant promise of one of the most exciting new voices to come out of the genre this century.

Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii

Author: David Carfi
Publisher: American Mathematical Soc.
ISBN: 0821891480
Size: 37.24 MB
Format: PDF, Mobi
View: 6163
Download Read Online

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: 19.60 MB
Format: PDF, ePub, Mobi
View: 3010
Download Read Online

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.

Maximum Entropy Information Without Probability And Complex Fractals

Author: Guy Jumarie
Publisher: Springer Science & Business Media
ISBN: 9401594961
Size: 36.37 MB
Format: PDF, Mobi
View: 7287
Download Read Online

Maximum Entropy Information Without Probability And Complex Fractals from the Author: Guy Jumarie. Every thought is a throw of dice. Stephane Mallarme This book is the last one of a trilogy which reports a part of our research work over nearly thirty years (we discard our non-conventional results in automatic control theory and applications on the one hand, and fuzzy sets on the other), and its main key words are Information Theory, Entropy, Maximum Entropy Principle, Linguistics, Thermodynamics, Quantum Mechanics, Fractals, Fractional Brownian Motion, Stochastic Differential Equations of Order n, Stochastic Optimal Control, Computer Vision. Our obsession has been always the same: Shannon's information theory should play a basic role in the foundations of sciences, but subject to the condition that it be suitably generalized to allow us to deal with problems which are not necessarily related to communication engineering. With this objective in mind, two questions are of utmost importance: (i) How can we introduce meaning or significance of information in Shannon's information theory? (ii) How can we define and/or measure the amount of information involved in a form or a pattern without using a probabilistic scheme? It is obligatory to find suitable answers to these problems if we want to apply Shannon's theory to science with some chance of success. For instance, its use in biology has been very disappointing, for the very reason that the meaning of information is there of basic importance, and is not involved in this approach.

Mathematica For Theoretical Physics

Author: Gerd Baumann
Publisher: Springer Science & Business Media
ISBN: 9780387251127
Size: 16.40 MB
Format: PDF, Mobi
View: 5335
Download Read Online

Mathematica For Theoretical Physics from the Author: Gerd Baumann. Class-tested textbook that shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Delivers dozens of fully interactive examples for learning and implementation, constants and formulae can readily be altered and adapted for the user’s purposes. New edition offers enlarged two-volume format suitable to courses in mechanics and electrodynamics, while offering dozens of new examples and a more rewarding interactive learning environment. Notebooks for problem solving and learning.

Applying Fractals In Astronomy

Author: Andre HECK
Publisher: Springer Science & Business Media
ISBN: 3540543538
Size: 62.53 MB
Format: PDF, ePub
View: 1667
Download Read Online

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 '.

Mathematica For Theoretical Physics

Author: Gerd Baumann
Publisher: Springer Science & Business Media
ISBN: 9780387251134
Size: 65.60 MB
Format: PDF, ePub, Mobi
View: 5870
Download Read Online

Mathematica For Theoretical Physics from the Author: Gerd Baumann. Class-tested textbook that shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Delivers dozens of fully interactive examples for learning and implementation, constants and formulae can readily be altered and adapted for the user’s purposes. New edition offers enlarged two-volume format suitable to courses in mechanics and electrodynamics, while offering dozens of new examples and a more rewarding interactive learning environment.

Quantum Mechanics Diffusion And Chaotic Fractals

Author: Mohammed S. El Naschie
Publisher:
ISBN: 9780080420271
Size: 64.84 MB
Format: PDF, ePub, Docs
View: 6524
Download Read Online

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.