Chaos: Classical and Quantum

Written by: Predrag Cvitanovic', Roberto Artuso, Ronnie Mainieri, Gregor Tanner, Gábor Vattay, Niall Whelan and Andreas Wirzba (Niels Bohr Institute, Copenhagen)

A group of scholars, who believed that most physics textbooks on “chaos” lack depth, joined forces to create a textbook which shows the “subject in its beauty and intellectual depth (that) ranks alongside statistical mechanics and quantum field theory, with which it shares many fundamental techniques.” Their text is 995 pages which, based on their rationale for creating a webbook, can only be expected to grow.

Predrag Cvitanovic’, Roberto Artuso, Ronnie Mainieri, Gregor Tanner, Gábor Vattay, Niall Whelan and Andreas Wirzba, Niels Bohr Institute, Copenhagen 2009 (with continual updates and revisions). A number of colleges and universities are using this free textbook in their classes.

One of the contributing authors, Predrag Cvitanovic, is a professor at the Georgia Institute of Technology. He offers an open online 2-part course course entitled Nonlinear Dynamics I & II: Geometry of Chaos. Students will use part one of the Chaos: Classical and Quantum textbook for part I of this course. The course is generally offered to PhD students, postdoctoral fellows and advanced undergraduates studying physics, mathematics, chemistry and engineering. Prerequisites include linear algebra, calculus, ordinary differential equations involving vectors and matrices, differentiate simple functions and an understanding of probability distribution. Prior exposure to Matlab, Octave or another programming language is helpful.

Table of Contents for Chaos: Classical and Quantum Textbook

I. Geometry of Chaos
1. Overture
2. Go with the flow
3. Discrete time dynamics
4. Local stability
5. Cycle stability
6. Lyapunov exponents
7. Hamiltonian dynamics
8. Billiards
9. World in a mirror
10. Relativity for cyclists
11. Charting the state space
12. Stretch, fold, prune
13. Fixed points, and how to get them
II. Chaos Rules
14. Walkabout: Transition graphs
15. Counting
16. Transporting densities
17. Averaging
18. Trace formulas
19. Spectral determinants
20. Cycle expansions
21. Discrete factorization
III. Chaos: what to do about it?
22. Why cycle?
23. Why does it work?
24. Intermittency
25. Deterministic diffusion
26. Turbulence?
27. Irrationally winding
IV. The rest is noise
28. Noise
29. Relaxation for cyclists
V. Quantum chaos
30. Prologue
31. Quantum mechanics, the short short version
32. WKB quantization
33. Semiclassical evolution
34. Semiclassical quantization
35. Quantum scattering
36. Chaotic multiscattering
37. Helium atom
38. Diffraction distraction
Epilogue
Index
VI. Web Appendices
A. A brief history of chaos
B. Go straight
C. Linear stability
D. Finding cycles
E. Symbolic dynamics techniques
F. Counting itineraries
G. Implementing evolution
H. Transport of vector fields
I. Discrete symmetries of dynamics
J. Convergence of spectral determinants
K. Infinite dimensional operators
L. Thermodynamic formalism
M. Statistical mechanics recycled
N. Noise/quantum corrections
S. Projects
S.1. Deterministic diffusion, zig-zag map
S.2. Deterministic diffusion, sawtooth map
   

View this Free Online Material at the source:
 
Chaos: Classical and Quantum


Real Time Web Analytics