From coherent to incoherent dynamical behaviour of quantum atomic gases in periodic potentials

In seminal experiments performed in 1995, alkali atomic gases have been cooled to nanokelvin temperatures to form a new state of matter which shows macroscopic quantum coherence and Bose-Einstein condensation. We give a physics-oriented view of diverse transport behaviours of these Bose-Einstein condensates, which can be explored after solving a nonlinear Schrodinger equation by means of an explicit time-marching algorithm. Coherent and decoherent transport behaviour in periodic potentials is reviewed and new aspects related to chaotic nonlinear dynamics are anticipated.