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FAKULTÄT FÜR PHYSIK Institut für Theoretische Physik Universität Regensburg · D-93040 Regensburg PD Dr. Juan Diego Urbina Telefon +49 941 943-2027 Sekretariat: Telefon +49 941 943-2030 Telefax +49 941 943-4382 Universitätsstraße 31 D-93053 Regensburg [email protected] www.physik.uni-regensburg.de/forschung winter term 2016/2017 Lectures on "Nonlinearity in Classical and Quantum Physics" (52414) PD Dr. Juan-Diego Urbina Description: In this lecture, we first go beyond the basic tools and concepts of classical mechanics, in order to go deeper into the structure and geometry of the phase space of Hamiltonian systems. This we do in order to define key concepts that describe the impact of non-linearity on the structure of the phase space, namely, integrability, its breaking due to perturbations, and the emergence of chaotic behavior. A natural question is therefore, where are the signatures of this transition on the quantum mechanical description? The very nature of this question demands to introduce techniques that allow us to connect the classical and quantum descriptions of physical phenomena. These techniques start with the path integral approach in quantum mechanics developed by Richard Feynman in the 60's, and by a set of transformations one obtains a description of the quantum dynamics in terms of classical paths, a great achievement of modern physics finalized by Martin Gutzwiller in the 70's. (Richard Feynman) (Martin Gutzwiller) In the second part of the lecture we then explain in detail how to use and manipulate path integrals in order to obtain this so-called semiclassical approximation. Finally, armed with the toolbox of semiclassical techniques, we address the impact of classical integrability and chaos on the quantum mechanical properties of Hamiltonian systems, a branch of Physics known as Quantum Chaos. 2 Requisites: We will need a basic knowledge of Lagrangian mechanics and quantum mechanics. Lectures: The lectures (Wednesdays and Fridays 8:00-10:00, H33) will be given in English, as well as the exercise sessions (to be decided between Mondays 16:00-18:00, PHY 9.2.01 and Thursdays 12:00-14:00, PHY 7.1.21). Exams: The final exam will consist of a single oral evaluation. A German-speaking person will be present. The precise date will be decided during the semester. Kontakt: PD Dr. Juan-Diego Urbina Institut für Theoretische Physik – Lst. Richter/Fabian PHY 4.1.31 Universität Regensburg, 93040 Regensburg +49-941-943-2027 3