Legacy of Alex Mueller

In my view the most important legacy of Alex Mueller is that he opened the Pandora’s box of complex strongly interacting systems including correlated electrons. In weakly interacting systems the perturbative field theories work well. But for strongly interacting systems theories cannot guide, and many surprising discoveries were made by experiments, with the high-temperature superconductivity to lead. I briefly discuss our recent work on another strongly interacting system, a liquid. Here the observation of strong medium-range order (MRO) and its role in viscosity led to the discovery of density wave instability in random systems. The competition between the density wave and atomic local order results in the MRO. I discuss its implications to superconductivity and relaxor ferroelectrics.