Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book 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 Focault 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.

Indubala I. Satija (with contributions by Douglas Hofstadter), George Mason University
Born in Amritsar, India, Indu Satija grew up in Bombay. After graduating with a Master's degree in physics from Bombay University, she came to New York to get her doctorate in theoretical physics at Columbia University. She is a physics professor at George Mason University in Fairfax, Virginia. She has published numerous scientific articles; this, however, is her first book. Physics is Indu's first love, and the outdoors is her second. She lives in Potomac, a suburb of Washington, DC, with her husband Sushil. Both Indu and Sushil are marathon runners, and they enjoy hiking and biking as well.

Table of Contents
Summary
About the Author
Preface
Prologue
Prelude

Part I: The butterfly fractal
0. Kiss precise
1. The fractal family
2. Geometry, number theory, and the butterfly: Friendly numbers and kissing circles
3. The Apollonian-butterfly connection (ABC)
4. Quasiperiodic patterns and the butterfly

Part II: Butterfly in the quantum world
5. The quantum world
6. A quantum-mechanical marriage and its unruly child

Part III: Topology and the butterfly
7. A different kind of quantization: The quantum Hall effect
8. Topology and topological invariants: Preamble to the topological aspects of the quantum Hall effect
9. The Berry phase and the quantum Hall effect
10. The kiss precise and precise quantization

Part IV: Catching the butterfly
11. The art of tinkering
12. The butterfly in the laboratory
13. The butterfly gallery: Variations on a theme of Philip G. Harper
14. Divertimento
15. Gratitude
16. Poetic Math & Science
17. Coda
18. Selected bibliography