Peaks of sound velocity in two color dense QCD: Quark saturation effects and semishort range correlations

We discuss stiffening of dense matter in two color QCD (QC$_2$D) where hadrons are mesons and diquark baryons. study models which describe a transition from the Bose-Einstein-Condensation regime at low density to Bardeen-Cooper-Schrieffer high density. The first model is based on coherent states diquarks, second Nambu-Jona-Lasinio with pairing terms. particularly focus how quark occupied as baryon increases. find that, due levels, ideal gas picture diquarks breaks down significantly less than cores overlap. saturation momenta stiffens equations state. also effects interactions depend occupation probability. argue that state become very stiff when bulk part Fermi sea has effective repulsion but surface enjoys attractive correlations. This disparity for different momentum domains possible strong channel dependence gluon exchanges transfer $0.2-1$ GeV. These concepts can be transferred QC$_2$D any numbers colors.