Classical and quantum investigations of four-dimensional maps with a mixed phase space
à 11h en salle C. BROT
Systems with more than two degrees of freedom are of fundamental importance for the understanding of problems ranging from celestial mechanics to molecules. Due to the dimensionality the classical phase-space structure of such systems is more difficult to understand than for systems with two or fewer degrees of freedom.
I will start the presentation with a remainder on the KAM theory of classical mechanics and an overview of ways to analyze the different types of dynamics in Hamiltonian Systems.
After this rather broad introduction I will summarize aspects of my PhD thesis covering 3d sections through the 4d phase space which reveal the regular and chaotic structures as well as methods based on frequency analysis.
Finally I will give an outlook on quantum-mechanical aspects of such systems including the consequences of the classical Arnold web and quantum mechanical tunneling couplings between regular and chaotic regions in phase space.
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