Berlin 2015 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 48: Quantum Chaos (jointly with DY)
TT 48.1: Vortrag
Dienstag, 17. März 2015, 14:30–14:45, BH-N 334
Regular phase-space structures and bifurcations in generic 4d symplectic maps — •Franziska Onken1, Steffen Lange1, Arnd Bäcker1,2, and Roland Ketzmerick1,2 — 1TU Dresden, Institut für Theoretische Physik, Dresden — 2MPI für Physik komplexer Systeme, Dresden
The dynamics of Hamiltonian systems (e.g., planetary motion, electron dynamics in nano-structures, molecular dynamics) can be investigated by symplectic maps. While a lot of work has been done for 2d maps, much less is known for higher dimensions.
For a generic 4d map regular 2d-tori are organized around a skeleton of families of elliptic 1d-tori [1], which can be visualized by 3d phase-space slices [2]. We present an analysis of the different bifurcations of the families of 1d-tori in phase space and in frequency space by computing the involved hyperbolic and elliptic 1d-tori. Applying known results of normal form analysis, both the local and the global structure can be understood: Close to a bifurcation of a 1d-torus, the phase-space structures are surprisingly similar to bifurcations of periodic orbits in 2d maps. Far away the phase-space structures can be explained by remnants of broken resonant 2d-tori.
[1] S. Lange, M. Richter, F. Onken, A. Bäcker and R. Ketzmerick, Global structure of regular tori in a generic 4D symplectic map, Chaos 24, 024409 (2014)
[2] M. Richter, S. Lange, A. Bäcker, and R. Ketzmerick, Visualization and comparison of classical structures and quantum states of four-dimensional maps, Phys. Rev. E 89, 022902 (2014)