We present a thorough numerical study of the Richardson model with quenched disorder (a fully-connected XX-model with longitudinal random fields). We study the onset of delocalization in typical states (many-body delocalization) and the delocalized p
hase which extends over the whole range of coupling strength in the thermodynamic limit. We find a relation between the inverse participation ratio, the Edwards-Anderson order parameter and the average Hamming distance between spin configurations covered by a typical eigenstate for which we conjecture a remarkably simple form for the thermodynamic limit. We also studied the random process defined by the spread of a typical eigenstate on configuration space, highlighting several similarities with hopping on percolated hypercube, a process used to mimic the slow relaxation of spin glasses.
Central Compact Objects (CCOs) are a handful of soft X-ray sources located close to the centers of Supernova Remnants and supposed to be young, radio-quiet Isolated Neutron Stars (INSs). A clear understanding of their physics would be crucial in orde
r to complete our view of the birth properties of INSs. We will review the phenomenologies of CCOs, underlining the most important, recent results, and we will discuss the possible relationships of such sources with other classes of INSs.
