Seminarium Fizyki Materii Skondensowanej

With the development of optical lattices a direct experimentalrealization of the quantum many-body theory models has become possible.One of the models realized with cold atomic lattices is the bosonicHubbard model. It describes a genuine competition between the itinerantbehavior of bosons, which leads to the formation of a Bose-Einsteincondensate, and a localizing effect of the interactionbetween particles. The dynamical mean-field approximation to the bosonic Hubbard model gives a comprehensive theoretical description ofcorrelated bosons in the superfluid and Mott-insulating phases. In thedynamical mean-field theory (DMFT), the lattice problem is replaced byan impurity coupled to dynamical self-consistent baths. The DMFT can beextended to treat inhomogeneous systems, which allows for studyingrealistic models of bosons in optically generated potentials. In theseminar I will present the theoretical framework of the DMFTapproximation for inhomogeneous systems and some preliminary results ofcomputations performed on Graphical Processing Units (GPUs).