The Butterfly in the Quantum World: The story of the most fascinating quantum fractal

ISBN-13: 9781681740539 / Angielski / Miękka / 2016 / 350 str.

Indubala I. Satija

Opis

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.

Spis treści

• 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