Introductory Chapter [to Superfluids and Superconductors]

This book deals with the recent advancements in two topical subjects of condensed mater physics, superluidity, and superconductivity. In principle, the two phenomena are very similar because they occur as a function of temperature and in the presence of the vanishing of a physical quantity marking a phase transition below a critical temperature. A superluid is a luid having zero viscosity while a superconductor is a conductor with zero resistance. Superluidity occurs in liquid helium and in ultracold atomic gases while superconductivity is typical of elements like niobium and lead, of some niobium alloys, or compounds like ytrium barium and copper oxide and compounds containing iron. Regarding the later, since the irst discoveries, the interplay between superconductivity and magnetism has also been investigated inding that the magnetic state of superconductors can be described as ideal diamagnetism. The behaviour toward the external magnetic ield allows to distinguish between irst- and second-type superconductors. Instead, the critical temperature in correspondence of which superconductivity arises allows to distinguish between low- and high-critical temperature superconductors. After their initial discovery, superluidity was explained as a quantum mechanical phenomenon, while superconductivity was described irst according to a phenomenological and classical theory and only in a second moment in terms of a microscopic quantum mechanical theory.