Dresden 2017 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 32: Quantum Chaos

DY 32.6: Hauptvortrag

Mittwoch, 22. März 2017, 11:30–12:00, HÜL 186

Semiclassical Classification of Periodic Orbits in Quantum Many-Body Systems — •Daniel Waltner, Maram Akila, Boris Gutkin, Petr Braun, and Thomas Guhr — Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47048 Duisburg

Classical periodic orbits on the one side and the quantum energy spectrum on the other are related in semiclassical theories by trace formulae. In the past, there has been huge interest in obtaining periodic orbit spectra for one-particle quantum systems (for example for the hydrogen atom in a strong magnetic field [1]). Here, the Fourier transformation of the trace formula was compared with the periodic orbits calculated by the classical equations of motion. In this talk, I demonstrate how to generalize this comparison to a many-particle system considering a kicked spin chain with nearest neighbor Ising coupling and on-site kicked magnetic field. Here, we face the problem that the dimension of the quantum Hilbert space and the number of periodic orbits is too large to apply the conventional methods used in [1]. We show how to overcome the problem arising from the large Hilbert space dimension by a duality relation and identify dominant contributions to the quantum spectrum arising from collective classical motion of the spins.

[1] D. Wintgen, Phys. Rev. Lett. 58, 1589 (1987).

[2] M. Akila, D. Waltner, B. Gutkin, P. Braun, T. Guhr, arXiv1611.05749.