Abstract

Localization of electrons characterizes the difference between an electrical insulator and a metallic conductor at low temperatures, and localization of atoms is one of the characteristics of a solid as opposed to a fluid. I discuss the suggestion made forty years ago that a quantum solid might be a supersolid with superfluid properties, and the recent experiments that show indications of superfluid properties in some solid helium samples. The behavior of the `center of mass’ of a system with periodic boundary conditions in one direction sheds light on the possibility of reduced moment of inertia in a solid. It seems unlikely that supersolidity is a property of a good crystal, but it has been argued that networks of dislocations or of grain boundaries could support a superfluid within real crystals.