Chiral Symmetry Restoration And Pion Superuidity At Finite Temperature And Density

The QCD phase structure is one of the most hottest topics in theoretical physics at finite temperature and finite baryon and isospin chemical potentials. It is an asymp-totically free theory. The interactions between quarks and gluons become weaker as the mutual distance decreases or as the exchanged momentum increases. QCD in-cludes many interesting problems, for example, the deconfinement phase transition, chiral symmetry restoration, quark-gluon plasma, color superconductivity and meson superfluidity. The general theoretical methods for studying QCD phase transitions are as follows:the perturbative QCD, the effective QCD models, lattice simulation and the recent AdS/CFT correspondence. The behavior of QCD at high temperature and low density is central to cosmology. The behavior of QCD at high density and low temper-ature is central to compact stars. The relativistic heavy ion collision at RHIC in USA and LHC in CERN provides an another way to detect the behavior of QCD for us. The research on phase transitions in strongly coupled matter at finite temperature and den-sity is very significant for our understanding of the real world. This thesis will cover two subjects:the quark potential mediated by mesons in a strongly coupled quark mat-ter, and the pion superfluidity and phase structure beyond mean field approximation in Nambu-Jona-Lasinio model.We investigate the effect of chiral symmetry restoration on quark potential in a strongly coupled quark matter by considering meson exchanges in the two flavor NJL model at finite temperature and density. There are two possible oscillations in the chiral restoration phase, one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the meson widths at high temperature. The quark-meson plasma is strongly coupled in the temperature region 1≤T/Tc≤3 with Tc being the critical temperature of chiral symmetry restoration. The maximum coupling in this region is located at the phase transition point.We investigate pion superfluidity and the phase structure in the frame of two fla- vor NJL model beyond mean field approximation. We calculate the thermodynamics to the next to leading order in an expansion in the inverse number of colors, includ-ing both quark and meson contributions at finite temperature and baryon and isospin density. The pions as Goldstone particles corresponding to spontaneous chiral sym-metry restoration do control the thermodynamic functions at low temperature and den-sity. Due to the meson fluctuations, the Sarma phase which exists at mean field level is washed away, and the Bose-Einstein condensation region at low isospin density is highly suppressed.