STATISTICAL MECHANICS II:
CHAOS, AND WHAT TO DO ABOUT IT 

INSTRUCTOR: Predrag Cvitanović
OFFICE: Howey W501
PHONE: 404/385-2502
EMAIL: predrag.cvitanovic@physics.gatech.edu
INSTRUCTOR HOMEPAGE: www.cns.gatech.edu/~predrag
COURSE HOMEPAGE: www.cns.gatech.edu/~predrag/courses/PHYS-7123-03
TIME: Fall semester 2003, TR 9:35-10:55
ROOM: Howey S106
EXPECTED ENROLLMENT: 15

COURSE DESCRIPTION: Graduate level introduction to modern theoretical physics and mathematics techniques for study of low-dimensional dynamical systems. The emphasis is on the interplay between the geometry and the statistical mechanics associated with the dynamics. The course has much in common with (and complements) graduate level field theory and statistical mechanics courses; partition functions and transfer operators are applied to computation of correlations and spectra of classical and quantum chaotic systems.
  • Historical perspective - chaos, and what to do about it.
  • Topology of flows - how to enumerate orbits, Smale horseshoes, entropy.
  • Dynamics, quantitative - periodic orbits, local stability.
  • Transfer operators - role of statistical distributions in dynamics.
  • Thermodynamic formalism - computing measurable averages over chaotic flows.
  • Spectroscopy of chaotic systems - evolution operators, zeta functions, cycle expansions.
    •  Arnold's cat,  by Leon Poon 
    The course is aimed at PhD students, postdoctoral fellows and advanced undergraduates in physics, mathematics, chemistry and engineering. A term project will take the place of a final exam. The term project will be individually tailored to student's level and research interests.

    e-TEXTBOOK: Chaos: Classical and Quantum webbook, available on www.cns.gatech.edu/ChaosBook. We will cover both the classical and quantum chaos in a 2-semester sequence (either part can be taken separately). The theory will be extended to quantum mechanics via Gutzwiller and Selberg trace formulas. This sequence is the last (?) prepublication test run of the web e-textbook. Your active participation in improving the book is very much encouraged.
    PREREQUISITES: A basic background in calculus, ordinary differential equations, classical, quantum and statistical mechanics. Weekly homework assignments require both analytic and numerical work, so familiarity with a programming language is a necessity.
    TEACHING METHOD: Two lectures and a homework problem set per week. For inspiration, consult www.cns.gatech.edu/ChaosBook/projects .
    EVALUATION METHOD: Weekly homework assignments and a term project individually tailored to student's level and research interests. Grades will be determined from the homework (60%) and the term project (40%).

    Even though the course number - phys 7123 - is the same, this course focuses on deterministic chaos, and has no overlap with Ron Fox fall 2002 course on stochastic and non-equilibrium processes.

    START: Tuesday Aug 19, 9:35 in Howey S106, with detailed schedule available on www.cns.gatech.edu/~predrag/courses/PHYS-7123-03/syllabus.html. Lecture topics will be described weekly by e-mail. Please subscribe to the course e-mail distribution even if you are only interested in a subset of the topics - send e-mail with text (and no header):
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