Dresden 2020 – wissenschaftliches Programm
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DY 39.9: Vortrag
Mittwoch, 18. März 2020, 17:30–17:45, HÜL 186
Quantum signatures of separatrix crossing: self-trapping in high dimensional Bose-Hubbard systems — •Mathias Steinhuber1, Steven Tomsovic2, Remy Dubertrand1, Klaus Richter1, and Juan-Diego Urbina1 — 1Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany — 2Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814, USA
We generalize the concept and phenomenology of self-trapping in the integrable Bose-Hubbard dimer into systems with non-integrable mean-field dynamics by relating it with crossing of separatrices. To this end, we construct a mapping of site-periodic solutions to find a sub-manifold of integrable dynamics in the non-integrable phase space. This new and powerful concept allows us to analytically explain the numerical observation of a massive transition in the stability properties of mean-field solutions found by Tomsovic in . We also show how this mapping has extensions and generalizations to higher dimensions, opening a door for analytical understanding beyond state of the art numerics, and obtain the Lyapunov spectra of site-periodic fix points, their stabilities and bifurcations. Last we show some quantum signatures of these morphology changes in the classical phases space focusing primarily on the self-trapping transition.
 Tomsovic, S. Complex saddle trajectories for multidimensional quantum wave packet and coherent state propagation: application to a many-body system. Phys. Rev. E 98, 023301 (2 Aug. 2018)