Quantum Chaos

Tel Aviv, Spring 2005

Zeev Rudnick

Schedule

Monday 10-12, Tueday 12-13, 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:
  1. Introduction to Number Theory.
  2. complex variables
  3. Real variables
  4. Probability theory

Bibliography

Some surveys:
  1. Stephan DeBievre Quantum chaos: a brief first visit Second Summer School in Analysis and Mathematical Physics (Cuernavaca, 2000), 161--218, Contemp. Math., 289, Amer. Math. Soc., Providence, RI, 2001.
  2. M V Berry Regular and Irregular Motion, in Topics in Nonlinear Mechanics, ed. S Jorna, Am.Inst.Ph.Conf.Proc No.46 (1978), 16-120.
  3. 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, North-Holland, Amsterdam 1983, p. 171-271

Contact me at: rudnick@post.tau.ac.il

Office : Schreiber 316, tel: 640-7806

Course homepage: http://www.math.tau.ac.il/~rudnick/courses/qc2005.html