Classical and Quantum Chaos
5
ECTS Credits
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Goals
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.The competencies of the students completing this course successfully would include understanding of basic concepts from both areas, familiarity with state-of-the art methods, and knowledge of examples of applications in the field of technology of mesoscopic and nano systems.
Curriculum
- 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.
Obligations
Completed Bologna second-cycle study program or an equivalent pre-Bologna university study program in the field of natural sciences or technology. Basic knowledge of mathematics and (possibly theoretical) physics is also required.Examination
Literature and references
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