- 量子世界中的蝴蝶--最迷人的量子分形故事(英文版)/国外优秀物理著作原版系列
- - 作者：(印)金杜·萨蒂亚|责编:杜莹雪//宋淼
  - 出版社：哈尔滨工业大学
  - ISBN：9787560388700
  - 出版日期：2020/07/01
  - 页数：356
- 售价：47.2

内容大纲
本书是有史以来第一本讲述“霍夫施塔特蝴蝶”的著作。研究了磁场中布洛赫电子的能级，从而发现了分形——“霍夫施塔特蝴蝶” 。“霍夫施塔特蝴蝶”是一个美丽而迷人的图形，位于物质量子理论的核心。在本书中，作者以完美的个人风格讲述了这个故事，并采用了大量丰富生动的历史轶事、照片、美丽的图像甚至诗歌，将本书变成一场饕餮盛宴，让你的眼睛、心灵和灵魂尽享科学的魅力，领略“霍夫施塔特蝴蝶”之美。
作者介绍
金杜·萨蒂亚（Indubala I.Satija）出生于印度，在孟买长大，从孟买大学获得物理学硕士学位后，她来到纽约，在哥伦比亚大学获得了理论物理学博士学位。目前，她是弗吉尼亚州费尔法克斯的乔治梅森大学的物理学教授，也是美国国家标准与技术研究所的物理学家。
目录
Summary
About the author
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
    References
  1  The fractal family
    1.1  The Mandelbrot set
    1.2  The Feigenbaum set
      1.2.1  Scaling and universality
      1.2.2  Self-similarity
    1.3  Classic fractals
      1.3.1  The Cantor set
      1.3.2  The Sierpinski gasket
      1.3.3  Integral Apollonian gaskets
    1.4  The Hofstadter set
      1.4.1  Gaps in the butterfly
      1.4.2  Hofstadter meets Mandelbrot
      1.4.3  Concluding remarks: A mathematical, physical, and poetic magt
     Appendix: Harper's equation as an iterative mapping
     References
     Geometry, number theory, and the butterfly: Friendly numbers and kissing circles
    2.1  Ford circles, the Farey tree, and the butterfly
      2.1.1  Ford circles
      2.1.2  Farey tree
      2.1.3  The saga of even-denominator and odd-denominator fractions
      2.1.4  The sizes of butterflies
    2.2  A butterfly at every scale--butterfly recursions
    2.3  Scaling and universality
      2.3.1  Flux scaling
      2.3.2  Energy scaling
      2.3.3  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
    References
  3  The Apollonian-butterfly connection (ABC)
    3.1  Integral Apollonian gaskets (IAG) and the butterfly
      3.1.1  A duality transformation
      3.1.2  Illustrating the Apollonian-butterfly connection
    3.2  The kaleidosoopic effect and trefoil symmetry
      3.2.1  Seeing an Apollonian gasket as a kaleidoscope

      3.2.2  How nested butterflies are related to kaleidoscopes
      3.2.3  ABC and trefoil symmetry
    3.3  Beyond Ford Apollonian gaskets and fountain butterflies
    Appendix: Quadratic Diophantine equations and IAGs
    References
  4   Quasiperioflic 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
    A.1  One-dimensional quasicrystals
    A.2  Two-dimensional quasicrystals: Quasiperiodic tiles
    A.3  A brief history of the discovery of quasicrystals
    A.4  Excerpts from the ceremony of the Nobel Prize in chemistry in 2011
    References
Part II  Butterfly in the quantum world
  5  The quantum world
    5.1  Wave or particle--what is it?
      5.1.1  Matter waves
    5.2  Quantization
    5.3  What is waving？--The Schr6dinger picture
    5.4  Quintessentially quantum
      5.4.1  The double-slit experiment, first hypothesized and finally realized
      5.4.2  The Ehrenberg-Siday-Aharonov-Bohm effect (ESAB)
    5.5  Quantum effects in the macroscopic world
      5.5.1  Central concepts of condensed-matter physics
      5.5.2  Summary
    References
  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 φ
    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 φ 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
     References
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 magne
      7.2.2  Quantum picture
      7.2.3  Semiclassical picture
    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
    References
  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
      8.2.1  Platonic solids
      8.2.2  Two-dimensional surfaces
      8.2.3  The Gauss-Bonnet theorem
    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
    References
  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
    References
  10  The kiss precise and precise quantization
    10.1  Diophantus gives us two numbers for each swath in the butterfly
      10.1.1  Quantum labels for swaths when φ is irrational
    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
    References
Part IV Catching the butterfly
  11  The art of tinkering
    11.1  The most beautiful physics experiments
    References
  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
    References
  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
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