Dresden 2011 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 24: Quantum Gases: Opt. Lattice 1
Q 24.10: Talk
Wednesday, March 16, 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 (ρ̂µ), two (ρ̂µν) and more lattice sites.
By complete induction, we prove a hierarchy of correlations such as ρ̂µνcorr = ρ̂µν − ρ̂µ ρ̂ν.
For large coordination numbers Z≫ 1, the two-point correlation ρ̂µνcorr is suppressed by ρ̂µνC = 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.