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Butterfly in the quantum world : the story of the most fascinating quantum fractal /
Butterfly in the Quantum World is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magn...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) :
Morgan & Claypool Publishers,
[2016]
|
| Colección: | IOP (Series). Release 3.
IOP concise physics. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 082 | 0 | 4 | |a 530.1201/514742 |2 23 |
| 100 | 1 | |a Satija, Indubala I., |d 1952- |e author. | |
| 245 | 1 | 0 | |a Butterfly in the quantum world : |b the story of the most fascinating quantum fractal / |c Indubala I. Satija ; with contributions by Douglas Hofstadter. |
| 246 | 3 | 0 | |a Story of the most fascinating quantum fractal. |
| 264 | 1 | |a San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : |b Morgan & Claypool Publishers, |c [2016] | |
| 264 | 2 | |a Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : |b IOP Publishing, |c [2016] | |
| 300 | |a 1 online resource (various pagings) : |b illustrations (chielfy color). | ||
| 336 | |a text |2 rdacontent | ||
| 337 | |a electronic |2 isbdmedia | ||
| 338 | |a online resource |2 rdacarrier | ||
| 490 | 1 | |a [IOP release 3] | |
| 490 | 1 | |a IOP concise physics, |x 2053-2571 | |
| 500 | |a "Version: 20160801"--Title page verso. | ||
| 500 | |a "A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso. | ||
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a Summary -- Preface -- Prologue -- Prelude -- part I. The butterfly fractal -- 0. Kiss precise -- 0.1. Apollonian gaskets and integer wonderlands -- Appendix. An Apollonian sand painting--the world's largest artwork | |
| 505 | 8 | |a 1. The fractal family -- 1.1. The Mandelbrot set -- 1.2. The Feigenbaum set -- 1.3. Classic fractals -- 1.4. The Hofstadter set -- Appendix. Harper's equation as an iterative mapping | |
| 505 | 8 | |a 2. Geometry, number theory, and the butterfly : friendly numbers and kissing circles -- 2.1. Ford circles, the Farey tree, and the butterfly -- 2.2. A butterfly at every scale--butterfly recursions -- 2.3. Scaling and universality -- 2.4. The butterfly and a hidden trefoil symmetry -- 2.5. Closing words : physics and number theory -- Appendix A. Hofstadter recursions and butterfly generations -- Appendix B. Some theorems of number theory -- Appendix C. Continued-fraction expansions -- Appendix D. Nearest-integer continued fraction expansion -- Appendix E. Farey paths and some comments on universality | |
| 505 | 8 | |a 3 The Apollonian-butterfly connection (ABC) -- 3.1 Integral Apollonian gaskets (IAG) and the butterfly -- 3.2 The kaleidoscopic effect and trefoil symmetry -- 3.3 Beyond Ford Apollonian gaskets and fountain butterflies -- Appendix. Quadratic Diophantine equations and IAGs | |
| 505 | 8 | |a 4. Quasiperiodic patterns and the butterfly -- 4.1. A tale of three irrationals -- 4.2. Self-similar butterfly hierarchies -- 4.3. The diamond, golden, and silver hierarchies, and Hofstadter recursions -- 4.4. Symmetries and quasiperiodicities -- Appendix. Quasicrystals | |
| 505 | 8 | |a part II. Butterfly in the quantum world -- 5. The quantum world -- 5.1. Wave or particle--what is it? -- 5.2. Quantization -- 5.3. What is waving?--The Schrödinger picture -- 5.4. Quintessentially quantum -- 5.5. Quantum effects in the macroscopic world | |
| 505 | 8 | |a 6. A quantum-mechanical marriage and its unruly child -- 6.1. Two physical situations joined in a quantum-mechanical marriage -- 6.2. The marvelous pure number [phi] -- 6.3. Harper's equation, describing Bloch electrons in a magnetic field -- 6.4. Harper's equation as a recursion relation -- 6.5. On the key role of inexplicable artistic intuitions in physics -- 6.6. Discovering the strange eigenvalue spectrum of Harper's equation -- 6.7. Continued fractions and the looming nightmare of discontinuity -- 6.8. Polynomials that dance on several levels at once -- 6.9. A short digression on INT and on perception of visual patterns -- 6.10. The spectrum belonging to irrational values of [phi] and the "ten-martini problem" -- 6.11. In which continuity (of a sort) is finally established -- 6.12. Infinitely recursively scalloped wave functions : cherries on the doctoral sundae -- 6.13. Closing words -- Appendix. Supplementary material on Harper's equation | |
| 505 | 8 | |a part III. Topology and the butterfly -- 7. A different kind of quantization : the quantum Hall effect -- 7.1. What is the Hall effect? Classical and quantum answers -- 7.2. A charged particle in a magnetic field : cyclotron orbits and their quantization -- 7.3. Landau levels in the Hofstadter butterfly -- 7.4. Topological insulators -- Appendix A. Excerpts from the 1985 Nobel Prize press release -- Appendix B. Quantum mechanics of electrons in a magnetic field -- Appendix C. Quantization of the Hall conductivity | |
| 505 | 8 | |a 8. Topology and topological invariants : preamble to the topological aspects of the quantum Hall effect -- 8.1. A puzzle : the precision and the quantization of Hall conductivity -- 8.2. Topological invariants -- 8.3. Anholonomy : parallel transport and the Foucault pendulum -- 8.4. Geometrization of the Foucault pendulum -- 8.5. Berry magnetism--effective vector potential and monopoles -- 8.6. The ESAB effect as an example of anholonomy -- Appendix. Classical parallel transport and magnetic monopoles | |
| 505 | 8 | |a 9. The Berry phase and the quantum Hall effect -- 9.1. The Berry phase -- 9.2. Examples of Berry phase -- 9.3. Chern numbers in two-dimensional electron gases -- 9.4. Conclusion : the quantization of Hall conductivity -- 9.5. Closing words : topology and physical phenomena -- Appendix A. Berry magnetism and the Berry phase -- Appendix B. The Berry phase and 2 x 2 matrices -- Appendix C. What causes Berry curvature? Dirac strings, vortices, and magnetic monopoles -- Appendix D. The two-band lattice model for the quantum Hall effect | |
| 505 | 8 | |a 10. The kiss precise and precise quantization -- 10.1. Diophantus gives us two numbers for each swath in the butterfly -- 10.2. Chern labels not just for swaths but also for bands -- 10.3. A topological map of the butterfly -- 10.4. Apollonian-butterfly connection : where are the Chern numbers? -- 10.5. A topological landscape that has trefoil symmetry -- 10.6. Chern-dressed wave functions -- 10.7. Summary and outlook | |
| 505 | 8 | |a part IV. Catching the butterfly -- 11. The art of tinkering -- 11.1. The most beautiful physics experiments | |
| 505 | 8 | |a 12. The butterfly in the laboratory -- 12.1. Two-dimensional electron gases, superlattices, and the butterfly revealed -- 12.2. Magical carbon : a new net for the Hofstadter butterfly -- 12.3. A potentially sizzling hot topic in ultracold atom laboratories -- Appendix. Excerpts from the 2010 Physics Nobel Prize press release | |
| 505 | 8 | |a 13. The butterfly gallery : variations on a theme of Philip G Harper -- 14. Divertimento -- 15. Gratitude 15-1 -- 16. Poetic math & science -- 17. Coda. | |
| 520 | 3 | |a Butterfly in the Quantum World is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? What energies can the electrons take on? From 1930 onwards, physicists struggled to answer this question, until 1974, when graduate student Douglas Hofstadter discovered that the answer was a graph consisting of nothing but copies of itself nested down infinitely many times. This wild mathematical object caught the physics world totally by surprise, and it continues to mesmerize physicists and mathematicians today. The butterfly plot is intimately related to many other important phenomena in number theory and physics, including Apollonian gaskets, the Foucault pendulum, quasicrystals, the quantum Hall effect, and many more. Its story reflects the magic, the mystery, and the simplicity of the laws of nature, and Indu Satija, in a wonderfully personal style, relates this story, enriching it with a vast number of lively historical anecdotes, many photographs, beautiful visual images, and even poems, making her book a great feast, for the eyes, for the mind and for the soul. | |
| 521 | |a Students, researchers, practitioners. | ||
| 530 | |a Also available in print. | ||
| 538 | |a Mode of access: World Wide Web. | ||
| 538 | |a System requirements: Adobe Acrobat Reader. | ||
| 545 | |a Indu Satija received her Masters in physics from Bombay University and her doctorate in theoretical physics from Columbia University. She is currently a physics professor at George Mason University where she researches topological insulators, Bose-Einstein condensates, and solitons. She has published numerous scientific articles and this is her first book. She lives in Potomac, a suburb of Washington, D.C., with her husband Sushil, a physicist at the National Institute of Standards and Technology. | ||
| 588 | |a Title from PDF title page (viewed on September 2, 2016). | ||
| 650 | 0 | |a Fractals. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Quantum theory. | |
| 650 | 7 | |a SCIENCE / Physics / Mathematical & Computational. |2 bicssc | |
| 650 | 7 | |a SCIENCE / Physics / Electromagnetism. |2 bicssc | |
| 650 | 7 | |a SCIENCE / Physics / Quantum Theory. |2 bicssc | |
| 650 | 7 | |a Mathematical physics. |2 bisacsh | |
| 650 | 7 | |a Quantum physics (quantum mechanics and quantum field theory) |2 bisacsh | |
| 650 | 7 | |a Electricity, electromagnetism and magnetism. |2 bisacsh | |
| 700 | 1 | |a Hofstadter, Douglas R., |d 1945- |e author. | |
| 710 | 2 | |a Morgan & Claypool Publishers, |e publisher. | |
| 710 | 2 | |a Institute of Physics (Great Britain), |e publisher. | |
| 776 | 0 | 8 | |i Print version: |z 9781681740539 |
| 830 | 0 | |a IOP (Series). |p Release 3. | |
| 830 | 0 | |a IOP concise physics. | |
| 856 | 4 | 0 | |u https://iopscience.uam.elogim.com/book/978-1-6817-4117-8 |z Texto completo |