Interplay of Correlations and Localization in Long-range Disordered Systems

In the last, but not the least direction, the main focus is on the localization effects in various long-range models (e.g., dipolar ones) which are relevant as for the experimental realizations in trapped ions and ultracold atoms as for the transistors in state-of-art computers. The latter are already close to the limit of the fully quantum transport and therefore are subjected to the disorder effects localizing electrons in thin films and narrow wires at any impurity concentration. Only due to electron-photon and electron-phonon scattering charges can still propagate at long-range distances in such wires and overcome localization effects. However, the correlations, anisotropy and time-reversal symmetry in long-range electron hopping crucially affect localization properties and may even localize almost all states in the system. This is the main topic of the above direction.