|We had promised to teach you something profound that your professor does not know. Well, this week is the week. If your professor knows cycle formulas for dynamical averages, please send us her name, and we'll feature it in ChaosBook. They look like cumulants, but when you start to evaluate them you realize that you would not guess their form in 1007 Phys. Rev. Letters. Takes 12 weeks of hard study to start to understand them.|
- 23. Cycle expansions
- 24. Deterministic diffusion
- Homework 12
Spectral eigenvalues and dynamical averages are computed by expanding spectral determinants into cycle expansions, expansions ordered by the topological lengths of periodic orbits. Skip sects. 23.3.1 "Newton algorithm for determining the evolution operator eigenvalues", and 23.6 "Stability ordering of cycle expansions".
We derive exact formulas for diffusion constants transport coefficients. All from first principles, without invoking any Boltzmann-Gibbs probabilistic notions. Read sect. 28.1: Foundations of statistical mechanics illuminated by 2-dimensional Lorentz gas.
| cycle expansion
Due 7 April 2015
|Discussion forum for week 12|
|Yasha Sinai gets Abel prize Sinai gets Abel Prize. Unexpectedly, Cvitanoviç nabs the coveted Night Fishing Champion trophy, to chagrin of the much more deserving Howey 3rd floor pros.|
|Chaos-theory pioneer Yakov Sinai nabs Abel Prize|
|Sinai billiard [animation by Oliver Knill, 26 March 2014]|
We are grateful Doug Eardley, KITP, Santa Barbara CA, for recording the lecture 23 videos.