Quantum Chaos
Tel Aviv, Spring 2005
Zeev Rudnick
Schedule
Monday 1012, Tueday 1213, Dan David 204
Course description
The course will cover a collection of problems associated with the
study of eigenvalues and eigenfunctions of certain operators occuring
in quantum mechanics of simple systems whose classical counterpart is
chaotic.
There are several interesting studies in the physics literature of the
statistical features of these systems, with very few mathematical
results. Even the apparently easier case of integrable systems poses
many unanswered problems.
We will learn a standard statistical model for these phenomena,
Random Matrix Theory, which gives some predictions to test.
We will also study these problems as they manifest themselves in some
special number theoretic models.
Prerequisites:
The course is intended for graduate students and advanced
undergraduates in mathematics. It assumes no knowledge of physics.
I assume knowledge of the contents of the following undergraduate
mathematics courses:

Introduction to Number Theory.
 complex variables
 Real variables
 Probability theory
Bibliography
Some surveys:

Stephan DeBievre
Quantum chaos: a brief first visit
Second Summer School in Analysis and Mathematical Physics
(Cuernavaca, 2000), 161218, Contemp. Math., 289, Amer. Math. Soc.,
Providence,
RI, 2001.
 M V Berry
Regular and Irregular Motion, in Topics in Nonlinear Mechanics, ed. S Jorna, Am.Inst.Ph.Conf.Proc No.46 (1978), 16120.
 M V Berry
Semiclassical Mechanics of regular and irregular motion ,
Les Houches Lecture series XXXVI,
eds. G Iooss, R H G Helleman and R Stora, NorthHolland, Amsterdam 1983,
p. 171271
Contact me at: rudnick@post.tau.ac.il
Office : Schreiber 316, tel: 6407806
Course homepage: http://www.math.tau.ac.il/~rudnick/courses/qc2005.html