MPŠ MP&Scaron MP&Scaron MP&Scaron Avtorji

Jo˛ef Stefan
Postgraduate School

Jamova 39
SI-1000 Ljubljana

Phone: +386 1 477 31 00
Fax: +386 1 477 31 10


Course Description

Classical and Quantum Chaos


Nanosciences and Nanotechnologies, third-level study programme


prof. dr. Marko Robnik


The aim is to acquaint the students with the basic concepts and theories of classical and quantum (wave) chaos, which have important and crucial applications in microscopic phenomena and structures such as atomic and molecular systems and nanostructures such as quantum dots.


· Introduction to classical chaos: integrability, nonlinearity, nonintegrability, KAM theory, ergodicity, statistical properties of classical motion, symbolic dynamics
· Introduction to semiclassical methods, WKB method, Gutzwiller theory (of periodic orbits)
· Random matrix theory and its application in various systems
· Introduction to quantum chaos: statistical properties of energy spectra, eigenfunction, Wigner functions, and matrix elements
· Dynamical quantum chaos and dynamic localization
· Applications: billiard systems, hydrogen atom in a strong magnetic field, wave chaos

Course literature:

M.C. Gutzwiller: Chaos in Classical and Quantum Mechanics, Springer, 1990
F. Haake, Quantum Signatures of Chaos, Springer, 2000
H.-J. Stöckmann, Quantum Chaos - an introduction, Cambridge University Press, 1999
R. Blümel and W.P. Reinhardt, Chaos in Atomic Physics, Cambridge University Press, 1997

Significant publications and references:

M. Robnik: Topics in quantum chaos of generic systems, Nonlinear Phenomena in Complex Systems (Minsk),Vol. 1, No. 1, 1-22 (1998)

T. Prosen and M. Robnik: Intermediate E(k,L) statistics in the regime of mixed classical dynamics, J. Phys. A: Math. Gen. Vol. 32, 1863-1873 (1999)

M. Robnik, Y. Aizawa, H. Hasegawa and Y. Kuramoto, Eds.: Let's Face Chaos through Nonlinear Dynamics, Proceedings of the 4th Int. Summer School/Conference held at CAMTP, University of Maribor, 1999: Progress of Theoretical Physics Supplement (Kyoto), No. 139, 1-557 (2000)


Type (examination, oral, coursework, project):
• seminar and oral exam

Students obligations:

• seminar and oral exam