Quark Matter At Finite Isospin Density

The phase structure and symmetries of strongly interacting matter have important significance in the study of Quantum Chromodynamics(QCD), its handling and the investigation of condensed states in QCD. For its rich symmetry structure, isospin matter is widely studied. High isospin density matter can be found in compact stars and low energy heavy ion collisions. Theoretically, Lattice QCD together with many e?ective models can be applied in the investigation of strong interaction matter at finite temperature and finite isospin chemical potential. In this thesis, we use a QCD e?ective modelNambu–Jona-Lasinio model to study chiral symmetry, isospin symmetry and UA(1) anomaly of QCD matter at finite temperature and finite isospin chemical potential. Based on mean field approximation, we studied the corresponding phase diagram.Beyond mean field approximation, we took Random Phase Approximation to construct e?ective mesonic propagator. Then we analyzed meson spectrum, quark-antiquark scattering phase shift, mesonic spectral function and topological susceptibility.Firstly, based on two-flavor NJL model, we studied chiral symmetry and isospin symmetry at finite temperature and finite isospin chemical potential. At low temperature and high isospin chemical potential, the system is in a phase of Pion superfluid with isospin symmetry spontaneously broken. In the superfluid phase, there exists a nonzero pseudoscalar condensate ˉuiγ5d, which leads to mixing of mean field u-d quark propagator and then mixing of e?ective mesonic propagator of modes π+-π--σ. We also redefined scattering phase shift and spectral function in Pion superfluid phase with mixed mesons,which can reasonably describe properties of the mixed mesons.Secondly, in the frame of three-flavor NJL model which includes UA(1) anomaly,we studied the e?ect of strange quark on the phase structure at finite temperature and finite isospin chemical potential. It shows that both in normal phase and superfluid phase,strange quark is coupled to light quarks, but the coupling strength is weak and it has little influence on the phase structure. In superfluid phase, nonzero pseudoscalar condensate mixes the light quarks, but strange quark is not mixed. UA(1) anomaly together with pseudoscalar condensate lead to complex mixing of mesonic propagators in superfluid phase. And also, we studied chiral symmetry and isospin symmetry and meson mixing in meson spectra analysis.At last, By comparing axial current equations in QCD and the three-flavor NJL model, we constructed e?ective topological charge density in NJL model, and also we derived expression for topological susceptibility at finite temperature and finite isospin chemical potential. The expression shows that topological susceptibility is closely related to chiral condensate, pseudoscalar condensate and UA(1) anomaly coupling coe?cient K. Numerical simulation shows that high isospin density leads to increase of topological susceptibility, and topological susceptibility reaches a minimum at critical point of superfluid phase transition at finite temperature and finite isospin chemical potential.