#14 Topology, disorder and cold atoms: when quantum becomes macro

In the presence of disorder, quantum systems present an absence of diffusion, thus becoming localised – this is the celebrated Anderson localisation. On the other hand, in periodic systems (such as crystals, optical lattices, etc.) the wave functions are periodic waves, extended through the entire system. Somewhere in between lies the case of quasi-periodic systems, which by presenting both disorder but also regularity, have both localised and extended states, the advantage being the fact that they are easily controllable, unlike in truly disordered systems.

These systems allow the study of many phenomena which involve localised states, allowing to emulate different physical systems. The fact that the localisation mechanism is weak and the energy spectrum is a fractal constitutes both a difficulty and a source of new effects.

The popularity of quasi-periodic systems has grown in the past decades, in both optics and atomic physics, with Bose-Einstein condensates (BECs) loaded into a quasi-periodic lattices an example. Since BECs present a non-linear behaviour, the interactions might lead to the emergence of novel behaviours, which moreover are macroscopic. Some interesting phenomena to study are the dynamics of few coupled localised modes as well as transport in moving lattices, where topology plays a big role.

Requirements: Some mild knowledge on mathematical and numerical methods