Dresden 2011 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 24: Quantum Gases: Opt. Lattice 1

Q 24.10: Vortrag

Mittwoch, 16. März 2011, 12:45–13:00, HSZ 02

Hierarchy of correlations in the Bose–Hubbard–Model — Ralf Schützhold, Patrick Navez, and •Markus Pater — Fakultät für Physik, Universität Duisburg-Essen, Lotharstaße 1, D-47057 Duisburg, Germany

We study the Bose–Hubbard–Model in terms of reduced density matrices of one (ρ̂_µ), two (ρ̂_µν) and more lattice sites.

By complete induction, we prove a hierarchy of correlations such as ρ̂_µν^corr = ρ̂_µν − ρ̂_µ ρ̂_ν.

For large coordination numbers Z≫ 1, the two-point correlation ρ̂_µν^corr is suppressed by ρ̂_µν^C = O ( 1/Z ) while three-point correlators are suppressed by O ( 1/Z² ) etc.

This facilitates a controlled analytical description of many–body quantum dynamics away from equilibrium.

We apply this approach to some physical example scenarios.