Erlangen 2018 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 18: Quantum Gases (Bosons) II

Q 18.5: Talk

Monday, March 5, 2018, 15:00–15:15, K 2.020

Periodic-Orbit Classification in Quantum Many-Body Systems — •Daniel Waltner, Maram Akila, Petr Braun, Boris Gutkin, and Thomas Guhr — Faculty of Physics, University of Duisburg-Essen, Duisburg, Germany

Semiclassical theories connect classical and quantum systems. They relate classical periodic orbits on the one side and the quantum spectrum on the other by trace formulae. In the past, there has been huge interest in obtaining periodic orbit spectra for single-particle quantum systems (for example for the hydrogen atom in a strong magnetic field and billiards). Here, the Fourier transformation of the trace formula was compared with the periodic orbits calculated by the classical equations of motion. In this presentation, 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 for single-particle systems. 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.
Reference: M. Akila, D. Waltner, B. Gutkin, P. Braun, T. Guhr, Phys. Rev. Lett. 118 (2017) 164101