Chiral Phase Transition In Equilibrium And Out-of-equilibrium System

A good microscopic theory presents high symmetries,however,due to the complicated interaction patterns,the macroscopic system usually presents low symmetries.The symmetry breaking is an effective way to bridge the gap between the micro theory and the macro system.The chiral symmetry is an important global symmetry of the quantum chromodynamics,it has huge impact on the structure of the strong interaction matter and the multi-body properties.In this thesis,we are going to investigate the chiral phase transition in equilibrium and non-equilibrium system in different ways.For the equilibrium systems,we adopt non-perturbative and beyond mean-field methods to demonstrate the importance of critical fluctuations and dynamical fluctuations in the phase transition.For the non-equilibrium systems,we adopt quantum transport theory to self-consistently investigate the mass effect in chiral magnetic effect and chiral phase transition in an expanding system.In the first part of the thesis,we discuss the chiral phase transition in an equilibrium system,and focus on the critical fluctuation and dynamical fluctuation.First,we investigate the QCD matter under finite isospin density in a non-perturbative framework.By solving the SU(2)functional renormalization group(FRG)flow equations,and analyzing the fixed point,we identify the universality class of the pion superfluid phase transition.We then study the spectral function of the meson excitation in pion superfluid system,and analyze the BEC-BCS crossover at finite isospin density.Second,we study the quark spectral function in the chiral phase transition in the framework of the FRG,and compare the result with the one-loop calculation.Third,we investigate the charged meson properties in the magnetic field.Starting from the Nambu–Jona-Lasinio model,we derive the meson effective Lagrangian in external magnetic field through bosonization and derivative expansion,and solve the problem of the Schwinger phase.The quark gluon plasma produced in heavy ion collision is crucial for the investigation of QCD matter in experiment.In order to compare the theory with experiment,it is required to study the out-of-equilibrium strong interaction matter.In the second part of this thesis,we study the chiral magnetic effect and chiral phase transition in the framework of quantum transport theory.We investigate the transport phenomenon of QCD matter in external magnetic field,we derive the chiral kinetic equation with small mass correction and study its influence in CME.We then study the chiral phase transition in an expanding system.By numerically solving the coupled transport equation and the gap equation,we self-consistently investigate the dependence of order parameter on time and space,as well as the evolution of the thermodynamical quantities.In the end,we give a brief summary and outlook.