The Influence Of Strong Magnetic Field On The Pion Superfluidity And Phase Structure In The NJL Model

Quantum chromodynamics(QCD) is a non-Abel gauge theory that describe the strong interaction between quarks and gluons, it is also a basic part of the stan-dard model of particle physics. QCD has a rich phase structure. There are three distinguished phases:the hadron phase, quark gluon plasma (QGP) and color super-conducting quark phase on the plane of temperature and chemical potential. QCD phase transition is due to the change of symmetry properties of the system, including the deconfinement phase transition, chiral phase transition, color superconducting phase transition,7r superfluid phase transition. This paper is focus on the influ-ence of the magnetic field on the pion superfluidity and the phase structure at finite temperature and finite isospin chemical potential in the framework of the two-flavor Nambu-Jona-Lasinio(NJL) model. Chiral phase transition, the π superfluid phase transition are related to this paper. Studing on the critical condition of QCD chiral symmetry restoration and transition mechanism has become an important aspect of exploring the nature of quark matter. The QCD phase structure, the phase boundary, the position of the QCD critical point are basic problems in this field.The influence of the magnetic field on the pion superfluidity and the phase struc-ture at finite temperature and finite isospin chemical potential is analyzed in the framework of the two-flavor NJL model. To do this, we first derive the thermody-namic potential from the Lagrangian density of the NJL model in the mean field approximation. Using this thermodynamic potential, we get the gap equations of the chiral condensate and the pion condensate. Then this paper is devoted to the numer-ical results of the quark pair condensation and the phase diagram in the T-μI-eB space. With the magnetic field considered, the tricritical point on the pion superflu-idity phase transition line moves to the space with smaller isospin chemical potential and higher temperature region. Considering the discrete of Landau Level, the influ-ence of the external magnetic field on the pion condensation is not simple promotion or suppression. In the end, the influence of external magnetic field on the chiral condensate is also studied.