Hannover 2016 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 46: Quantum Gases: Bosons V
Q 46.3: Vortrag
Donnerstag, 3. März 2016, 11:30–11:45, e001
Spectral characterization of two-dimensional Bose-Hubbard models — •David Fischer1, Darius Hoffmann1, and Sandro Wimberger1,2,3 — 1Institut für Theoretische Physik, Universität Heidelberg, 69120 Heidelberg, Germany — 2Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Parma, Via G. P. Usberti 7/a, 43124 Parma — 3INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, Italy
We study the spectral properties of simple Bose Hubbard models in two dimensions. Small finite size lattices are analyzed for different boundary conditions and different geometries. As we will show, the chosen geometry determines the level-spacing-statistics, which we investigate numerically for all symmetry-reduced subspaces of the Hamiltonian matrix. By comparison of both next-neighbor statistics and long-range spectral correlation functions with the predictions from Random-Matrix Theory (RMT), we find that most setups enjoy quantum chaotic behavior in a certain regime of parameters. This coincides with previous results for one-dimensional systems. Increasing the number of bonds in the lattice results in a smooth transition to a more regular behavior over the whole parameter range. Our spectral results allow us to control the systems’ dynamics in a desired way by the choice of the specific form of the lattice and its bonds. Moreover, our investigations may enable further studies of quantum many-body chaos, which is becoming more and more relevant also for state-of-the-art experiments with ultracold bosons in optical lattices.