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DY: Fachverband Dynamik und Statistische Physik
DY 8: Superfluidity and Bose Einstein Condensation
DY 8.4: Vortrag
Montag, 25. Februar 2008, 17:45–18:00, MA 001
Green’s Function Approach to the Bose-Hubbard Model for Finite Temperatures — Henrik Enoksen1, •Alexander Hoffmann2, Matthias Ohliger3, and Axel Pelster4 — 1Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway — 2Arnold Sommerfeld Center for Theoretical Physics, Theresienstr. 37, Department Physik, Universität München, 80333 München, Germany — 3Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany — 4Fachbereich Physik, Universität Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany
The Green’s function for bosons in an optical lattice is determined in the Mott phase within a finite-temperature hopping expansion up to the second order in the tunnel matrix element. This allows us to reconstruct in a qualitative way the time-of-flight absorption pictures, which are taken after the optical lattice is switched off. Furthermore, investigating the divergence of the Green’s function, we can locate the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by Monte-Carlo simulations of the Bose-Hubbard model.