Butterfly in the quantum world : the story of the most fascinating quantum fractal
著者
書誌事項
Butterfly in the quantum world : the story of the most fascinating quantum fractal
（IOP concise physics）（IOP ebooks）
Morgan & Claypool Publishers, c2016
- : hardback
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注記
"Version: 20160801"--t.p.verso
"A Morgan & Claypool publication as part of IOP Concise Physics"--t.p.verso
Includes bibliographical references
内容説明・目次
内容説明
Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, 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.
目次
Prelude
Kiss precise
The fractal family
Geometry, number theory, and the butterfly: Friendly numbers and kissing circles
The Apollonian-butterfly connection (ABC)
Quasiperiodic patterns and the butterfly
The quantum world
A quantum-mechanical marriage and its unruly child
A different kind of quantization: The quantum Hall effect
Topology and topological invariants: Preamble to the topological aspects of the quantum Hall
The Berry phase and the quantum Hall effect
The kiss precise and precise Quantization
The art of tinkering
The butterfly in the laboratory
Gallery
Divertimento
Gratitude
Poetic
Coda
Selected Bibliography
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