Paperback (ISBN-13: 9780521031660 | ISBN-10: 0521031664)
Hardback (ISBN-13: 9780521432917 | ISBN-10: 052143291X)
Quantum Chaos provides a comprehensive overview of our
understanding of chaotic behaviour in a wide variety of quantum
and semiclassical systems, and describes both experimental and
theoretical investigations. A general introduction sets out the
main features of chaos in quantum systems. Thereafter, in an
authoritative collection of papers, prominent scientists put
forward their particular interpretations of quantum chaos, with
reference to a broad range of interesting physical systems. As
yet, there is no universally accepted definition of quantum chaos.
However, by dealing with such a wide range of topics from
different branches of physics, this book provides a unique
overview of this rapidly expanding field, and will be of great
interest to graduate students and researchers in many areas of
physics and chemistry.
* Unique breadth of coverage
* Detailed introductory chapter by the editors
* Chaos and nonlinear dynamics are two of the hottest subjects in
science right now
Contents
Preface; Acknowledgments; Introduction: 1. The legacy of chaos in
quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical
Chaos and Quantum Localization: 2. Stochastic behaviour of a
quantum pendulum under a periodic perturbation G. Casati, B. V.
Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a
nonintegrable system D. R. Grempel, R. E. Prange and S. E.
Fishman; 4. Excitation of molecular rotation by periodic
microwave pulses. A testing ground for Anderson localization R.
Blumel, S. Fishman and U. Smilansky; 5. Localization of diffusive
excitation in multi-level systems D. K. Shepelyansky; 6.
Classical and quantum chaos for a kicked top F. Haake, M. Kus and
R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl
and L. Haoming; 8. Time irreversibility of classically chaotic
quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent
quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10.
Dynamical localization, dissipation and noise R. F. Graham; 11.
Maximum entropy models and quantum transmission in disordered
systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in
intense oscillating fields M. S. Sherwin; Part II. Atoms in
Strong Fields: 13. Localization of classically chaotic diffusion
for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati,
I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport
due to 'scars' of unstable periodic orbits R. V. Jensen, M. M.
Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms
in strong fields G. Benson, G. Raithel and H. Walther; 16.
Diamagnetic Rydberg atom: confrontation of calculated and
observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner,
D. Delande and J. C. Gay; 17. Semiclassical approximation for the
quantum states of a hydrogen atom in a magnetic field near the
ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The
semiclassical helium atom D. Wintgen, K. Richter and G. Tanner;
19. Stretched helium: a model for quantum chaos in two-electron
atoms R. Blumel and W. P. Reinhardt; Part III. Semiclassical
Approximations: 20. Semiclassical theory of spectral rigidity M.
V. Berry; 21. Semiclassical structure of trace formulas R. G.
Littlejohn; 22. h-Expansion for quantum trace formulas P.
Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P.
Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm
breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky;
25. Semiclassical propagation: how long can it last? M. A.
Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized
Baker's transformation N. L. Balazs and A. Voros; 27. Classical
structures in the quantized baker transformation M. Saraceno; 28.
Quantum nodal points as fingerprints of classical chaos P.
Leboeuf and A. Voros; 29. Chaology of action billiards A. M.
Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level
Statistics and Random Matrix Theory: 30. Characterization of
chaotic quantum spectra and universality of level fluctuation
laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum
chaos, localization and band random matrices F. M. Izrailev; 32.
Structural invariance in channel space: a step toward
understanding chaotic scattering in quantum mechanics T. H.
Seligman; 33. Spectral properties of a Fermi accelerating disk R.
Badrinarayanan and J. J. Jose; 34. Spectral properties of systems
with dynamical localization T. Dittrich and U. Smilansky; 35.
Unbound quantum diffusion and fractal spectra T. Geisel, R.
Ketzmerick and G. Petschel; 36. Microwave studies in irregularly
shaped billiards H.-J. Stockmann, J. Stein and M. Kollman; Index.
Paperback (ISBN-13: 9780521663939 | ISBN-10: 0521663938)
Cambridge University's Lucasian Professorship of Mathematics is
one of the most celebrated academic positions in the world. Since
its foundation in 1663, the chair has been held by seventeen men
who represent some of the best and most influential minds in
science and technology. Principally a social history of
mathematics and physics, the story of these great natural
philosophers and mathematical physicists is told here by some of
the finest historians of science. The journey begins with the
search for a benefactor able to establish a 'mathematicus
professor honorarius', and travels through the life and work of
the professors, exploring aspects from the heroic to the absurd.
Covering both the great similarities and the extreme differences
in mathematical physics over the last four centuries, this
informative work offers new perspectives on world-famous
scientists including Isaac Newton, Charles Babbage, G. G. Stokes,
Paul Dirac and Stephen Hawking.
* Places well-known scientists within the broad and complex
history of the Lucasian Professorship of Mathematics
* Emphasises the interplay between mathematics, natural
philosophy, politics and religion inside and outside Cambridge
University
* Written by leading historians of science, including a foreword
by Stephen Hawking
Contents
Timeline of Lucasian Professors; Foreword Stephen Hawking;
Introduction: 'Mind Almost Divine' K. C. Knox and R. Noakes; 1.
Isaac Barrow and the foundation of the Lucasian Professorship M.
Feingold; 2. 'Very Accomplished Mathematician, Philosopher,
Chemist' - Newton as Lucasian Professor R. Iliffe; 3. Making
Newton easy: William Whiston in Cambridge and London S. Snobelen
and L. Stewart; 4. Sensible Newtonians: Nicholas Saunderson &
John Colson J. Gascoigne; 5. The negative side of nothing: Edward
Waring, Isaac Milner and Newtonian values K. C. Knox; 6. Paper
and brass: The Lucasian Professorship 1820-1839 S. Schaffer; 7.
Arbiters of Victorian science: George Gabriel Stokes and Joshua
King D. B. Wilson; 8. 'That Universal Aetherial Plenum': Joseph
Larmor's Natural History of Physics A. Warwick; 9. Paul Dirac:
the purest soul in an atomic age H. Kragh; 10. Is the end in
sight for the Lucasian Chair? Stephen Hawking as Millennium
Professor H. Mialet; Appendix. The Statutes of the Lucasian
Professorship: a translation I. Stewart.
Series: Collection Alea-Saclay: Monographs and Texts in
Statistical Physics
Paperback (ISBN-13: 9780521031875 | ISBN-10: 0521031877)
This book shows how the concept of geometrical frustration can be
used to elucidate the structure and properties of non-periodic
materials such as metallic glasses, quasicrystals, amorphous
semiconductors and complex liquid crystals. Geometric frustration
is introduced through examples and idealized models, leading to a
consideration of how the concept can be used to identify ordered
and defective regions in real materials. Then it is shown how
these principles can also be used to model physical properties of
materials, in particular specific volume, melting, the structure
factor and the glass transition. Final chapters consider
geometric frustration in periodic structures with large cells and
quasiperiodic order. Appendices give all necessary background on
geometry, symmetry and tilings. The text considers geometrical
frustration at different scales in many types of materials and
structures, including metals, amorphous solids, liquid crystals,
amphiphiles, cholisteric systems, polymers, phospholipid
membranes, atomic clusters, and quasicrystals. Of interest to
researchers in condensed matter physics, materials science and
structural chemistry, as well as mathematics and structural
biology.
* Topical area
* Accessible and well-illustrated account
* Of interest to wide group of researchers in condensed matter
physics, materials science, structural chemistry, mathematics and
structural biology
Contents
Preface; 1. Introduction to geometrical frustration; 2. Ideal
models; 3. Finite structures; 4. Decurving and disclinations; 5.
Hierarchical polytopes; 6. Some physical properties; 7. Periodic
structures with large cells; 8. Quasiperiodic order and
frustration; Appendices; Bibliography; Index.
Series: Analytical Methods for Social Research
Paperback (ISBN-13: 9780521686891 | ISBN-10: 052168689X)
Hardback (ISBN-13: 9780521867061 | ISBN-10: 0521867061)
Data Analysis Using Regression and Multilevel/Hierarchical Models
is a comprehensive manual for the applied researcher who wants to
perform data analysis using linear and nonlinear regression and
multilevel models. The book introduces a wide variety of models,
whilst at the same time instructing the reader in how to fit
these models using available software packages. The book
illustrates the concepts by working through scores of real data
examples that have arisen from the authors' own applied research,
with programming codes provided for each one. Topics covered
include causal inference, including regression,
poststratification, matching, regression discontinuity, and
instrumental variables, as well as multilevel logistic regression
and missing-data imputation. Practical tips regarding building,
fitting, and understanding are provided throughout.
* Discusses a wide range of linear and non-linear multilevel
models
* Provides R and Winbugs computer codes and contains notes on
using SASS and STATA
* Analyses illustrated with dozens of graphs of data and fitted
models
* Dozens of examples, almost all coming from Gelman/Hill's own
applied research
Contents
1. Why?; 2. Concepts and methods from basic probability and
statistics; Part IA. Single-level Regression: 3. Linear
regression: the basics; 4. Linear regression: before and after
fitting the model; 5. Logistic regression; 6. Generalized linear
models; Part IB. Working with Regression Inferences: 7.
Simulation of probability models and statistical inferences; 8.
Simulation for checking statistical procedures and model fits; 9.
Causal inference using regression on the treatment variable; 10.
Causal inference using more advanced models; Part IIA. Multilevel
Regression: 11. Multilevel structures; 12. Multilevel linear
models: the basics; 13. Multilevel linear models: varying slopes,
non-nested models and other complexities; 14. Multilevel logistic
regression; 15. Multilevel generalized linear models; Part IIB.
Fitting Multilevel Models: 16. Multilevel modeling in bugs and R:
the basics; 17. Fitting multilevel linear and generalized linear
models in bugs and R; 18. Likelihood and Bayesian inference and
computation; 19. Debugging and speeding convergence; Part III.
From Data Collection to Model Understanding to Model Checking: 20.
Sample size and power calculations; 21. Understanding and
summarizing the fitted models; 22. Analysis of variance; 23.
Causal inference using multilevel models; 24. Model checking and
comparison; 25. Missing data imputation; Appendixes: A. Six quick
tips to improve your regression modeling; B. Statistical graphics
for research and presentation; C. Software; References.
Paperback (ISBN-13: 9780521700849 | ISBN-10: 0521700841)
Grab a pencil. Relax. Then take off on a mind-boggling journey to
the ultimate frontier of math, mind, and meaning as acclaimed
author Dr Clifford Pickover, Dorothy, and Dr Oz explore some of
the oddest and quirkiest highways and byways of the numerically
obsessed. Prepare yourself for a shattering odyssey as The
Mathematics of Oz unlocks the doors of your imagination. The
thought-provoking mysteries, puzzles, and problems range from
zebra numbers and circular primes to Legion's number - a number
so big that it makes a trillion pale in comparison. The strange
mazes, bizarre consequences, and dizzying arrays of logic
problems will entertain people at all levels of mathematical
sophistication. The tests devised by enigmatic Dr Oz to assess
human intelligence will tease the brain of even the most avid
puzzle fan. Test your wits on a host of mathematical topics:
geometry and mazes, sequences, series, sets, arrangements,
probability and misdirection, number theory, arithmetic, and even
several problems dealing with the physical world. With numerous
illustrations, this is an original, fun-filled, and thoroughly
unique introduction to numbers and their role in creativity,
computers, games, practical research, and absurd adventures that
teeter on the edge of logic and insanity. The Mathematics of Oz
will have you squirming in frustration and begging for more.
* Big name author who has written over 20 popular books plus
puzzle columns for Discover and other popular magazines
* New and unusual mathematical puzzles not found in standard
collections
* Lots of amusing original illustrations
Contents
Travel guide; Preface; Introduction; Puzzles: 1. The yellow-brick
road; 2. Animal array; 3. An experiment with Kansas; 4. An
experiment with signs; 5. The logic of greenness; 6. Magical
maze; 7. Kansas railway contraction; 8. The problem of the bones;
9. Square overdrive; 10. Squares and cubes; 11. Plex's matrix; 12.
Chaos at the clock factory; 13. The upsilon configuration; 14.
Bone toss; 15. Animal farm courthouse; 16. Omega sphere; 17. Leg
bone shatter produces triangle; 18. Z-bar ranch; 19. Mystery of
phasers; 20. Salty number cycle; 21. Where are the composites?;
22. Brain trip; 23. The gaps of omicron; 24. Hutchinson problem;
25. Flint hill series; 26. Wacky tiles; 27. Toto clone puzzle; 28.
Legion's number; 29. The problems of the tombs; 30. Plex's tiles;
31. Phasers on targets; 32. The chamber of death and despair; 33.
Zebra irrationals; 34. Creatures in resin; 35. Prime-poor
equations; 36. Number satellite; 37. Flatworm math; 38. Regolith
paradox; 39.; 40. Entroy; 41. Animal gap; 42. Arranging alien
heads; 43. Ramanujan congruences and the quest for transcendence;
44. Getting noticed; 45. Juggler numbers; 46. Friends from Mars;
47. Phi in four 4s; 48; On planet zyph; 49. The jellyfish of
europa; 50. Archeological dissection; 51. The gamma gambit; 52.
Robot hand hive; 53. Ramanujan and the quattuordecillion; 54.
Lunatic ferris wheel; 55. The ultimate spindle; 56. Prairie
artifact; 57. Alien pellets; 58. The beauty of polygon slicing;
59. Cosmic call; 60. Knight moves; 61. Sphere; 62. Potawatomi
target; 63. Sliders; 64. Swapping; 65. Triangle dissection; 66. A
simple code; 67. Heterosquare; 68. Insertion; 69. Missing
landscape; 70. The choice; 71. Animal selection; 72. The skeletal
men of Uranus; 73. Hindbrain stimulation; 74. The arrays of
absolution; 75. Trochophore abduction; 76. The dream pyramids of
Missouri; 77. Mathematical flower petal; 78. Blood and water; 79.
Cavern problems; 80. Three triplets; 81. Oos and oob gambit; 82.
Napiform mathematics; 83. Toto, Mr. plex, elephant; 84. Witch
overdrive; 85. What is art?; 86. Wendy magic square; 87. Heaven
and hell; 88. The stars of heaven; 89. Vacation in the Tarantula
nebula; 90. Hot lava; 91. Circular primes; 92. The truth about
cats and dogs; 93. Disc mania; 94. N2+m2=s; 95. 2, 271, 2718281;
96. Android watch; 97. Knight moves; 98. Pool table gambit; 99. A
connection between pi and e; 100. Venusian number bush; 101.
Triangle cave; 102. Rat attack; 103. The scarecrow formula; 104.
Circle math; 105. A, AB, ABA; 106. Ants and cheese; 107. The
omega crystal; 108. Attack of undulating undecamorphs; Epilog;
Further exploring; For further reading; About the author.