Research On Two-flavor Non-uniform Neutral Color Superconductivity

In the core of a Neutron star, the density of nuclear matter is compressed as several times dense as the normal nuclear matter by the gravitational field. According to the bag model,the nucleons will overlap to form quark matter. Quantum Chromo-dynamics (QCD) is regarded as the fundamental theory of quarks and gluons which predicts that the quark matter at low temperature and high density is color supercon-ductivity(CSC). So the research of CSC is important for the exploration of Neutron star physics as well as the seeking of quark stars in universe. As the lattice QCD can't be used in the QCD of high density, there are mainly two approaches to study CSC:(a)Perturbative QCD(PQCD), which is suitable to quark matter at very high energies,where the Fermi energy of quark matter is much larger than∧_QCD. Because of the asymptotically freedom of QCD ,the coupling is weak at very high density. And the pairing mechanism in this condition is through single gluon exchange. (b)NJL model. It is suitable to moderate baryon density regime which is the possible density in the core of a Neutron star. And the Fermi energy is two or three times dense as the∧_QCD. The reliability of PQCD calculations is difficult to estimate. In the research of CSC, we have to rely on NJL model,where the pairing mechanism comes from instanton effect.Nonzero strange quark mass or the requirement of charge neutrality induces a mismatch between the Fermi momenta of the two pairing quarks, therefore CSC has very rich phase structures, including Gapless phase,LOFF phase the mix phase of BCS-NORMAL. But there are still dispution on the ground state of CSC quark matter.This article focuses on the two-flavor color superconductivity phase at moderate baryon density. Starting from SU(2) NJL model, we describe numerically a LOFF state satisfying the color and electric neutrality conditions in weak coupling region where neither the neutral 2SC nor neutral g2SC exist . We also show that the neutral LOFF is free from chromomagnetic instabilities in weak coupling , whereas in middling coupling region the neutral LOFF suffers from chromomagnetic instabilities. Different from the ideal CSC, the Fermi momentum of the pairing quarks in the LOFF are not equal. For suitable values of the differences between chemical potentials, Cooper pairs have nonzero total momentum and each of the two quarks in a pair can be close to its Fermi surface, and such pairs can be created at low cost in free energy.The thesis consists of three parts. The first part is a brief review of Finite-Temperature Field Theory. In the second part, we first introduce the basic knowledge of color superconductivity and the its research developments ,then we discuss the thermodynamics of a system with strong restriction. In the third part, LOFF state is described numerically satisfying the color and electric neutrality conditions both in weak coupling and in middling coupling regions.