Superfluidity, superconductivity and magnetism in mesoscopics

The nature of superfluid, superconducting, and magnetic ordering is elucidated for mesoscopic systems in which the single-particle level spacing is much larger than both the temperature and the critical temperature of ordering. Ordering is defined as a spontaneous violation of symmetry, the gauge invariance and time reversal being by definition symmetries violated in superfluidity (superconductivity) and magnetism contexts, respectively. Superfluidity and superconductivity are realized in thermodynamic equilibrium states with a non-integral average number of particles and are accompanied by the spontaneous violation of time homogeneity. In Fermi systems two types of superfluidity and superconductivity are possible which are characterized by the presence of pair or single-particle 'condensates'. The latter is remarkable in that spontaneous violation of fundamental symmetries such as spatial 2π rotation and double time reversal takes place. Possible experiments on metallic nanoparticles and ultracold atomic gases in magnetic traps are discussed.