Superfluidity in nuclear systems and neutron stars.

Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs due to the attractive component of the nuclear interaction. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spacially extended ensembles encountered in neutron stars and in nuclear collisions. Our survey includes techniques which are based on Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. Novel phases arise in nuclear and related systems (such as ultra-cold atomic gases) under imbalance in the populations of the fermions that form Cooper pairs. Such phases include current-carrying superfluid states, heterogeneous phase-separated states, and phases involving deformation of Fermi surfaces. The phase diagram of imbalanced superfluids is reviewed, focusing especially on the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound dimers under increase of the coupling strength of the theory. The neutron, proton, and hyperonic condensates that may exist under conditions prevailing in neutron stars are discussed, and calculations of weak-interaction rates within the Green functions formalism are examined in detail. We close with a discussion of quantum vortex states in nuclear systems and their dynamics in neutron-star crusts.