Regensburg 2016 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 41: Quantum Chaos

DY 41.1: Hauptvortrag

Mittwoch, 9. März 2016, 15:00–15:30, H48

Visualizing quantum chaos in four dimensions — •Arnd Bäcker — TU Dresden, Institut für Theoretische Physik and Center for Dynamics, Dresden — MPI für Physik komplexer Systeme, Dresden

As the simplest example of higher-dimensional systems with a mixed phase space we consider 4d maps. The global organization of regular tori is visualized using 3d phase-space slices [1, 3]. Representing regular and chaotic eigenstates in the 3d phase-space slice allows for comparing with classical structures to investigate the semiclassical eigenfunction hypothesis.

Such 4d maps can also be interpreted as two coupled 2d systems. If these two subsystems are strongly chaotic, we demonstrate that spectral statistics show a universal transition towards random matrix fluctuations for increasing interaction strength [2]. Moreover, entanglement in eigenstates, as measured by the von-Neumann entropy, shows a universal transition to nearly maximal entanglement.

[1] 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).

[2] S. C. L. Srivastava, S. Tomsovic, A. Lakshminarayan, R. Ketzmerick, and A. Bäcker, Universal scaling of spectral fluctuation transitions for interacting chaotic systems, arXiv:1509.02329, Phys. Rev. Lett. in press.

[3] For videos of 3d phase space slices see:
http://www.comp-phys.tu-dresden.de/supp/