Download Nonlinearity in Classical and Quantum Physics

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.
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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
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