New challenges of AMO physics?

Maciej Lewenstein

Intitute for Theoretial Physics, Universität Hannover, Appelstr. 2, 30419 Hannover, Germany

I will present a review of recent developents in physics of ultracold atomic and molecular gases in optical lattices. Such systems are described by various types of Hubbard models and are analogous, or sometimes reacher than those investigated in condensed matter physics. Such sytems may serve as experimentally physible quantum simulators of the Hubbard models,or maybe of fundamental interest themselves, exhibiting novel froms of quantum states of matter. I will in particular discuus in details physics of mixtures, physics of disordered systems with controllable disorder, realisations of systems with exotic geometries, and simulations of lattice non-abelian gauge fields.