The Fluctuation And Excitation In Color Superconductivity

The dense quark matter at low temperature plays an important role in con-struction of the Quantum Chromodynamics (QCD) phase diagram. Due to the presence of the anti-symmetric and attractive channel in quark-quark interaction and the Fermi surface, two quarks on the Fermi surface can form Bardeen-Cooper-Schrieffer (BCS) state with an energy gap. It is a new state of matter similar to superconductivity in metals and thus is called color superconductivity.The BCS variational method can be used to calculate the energy gap and other quantities of a color superconductor. Renormalization group method and Nambu-Jona-Lasinio (NJL) model can also give the properties of the color super-conductor. Spontaneously symmetry breaking in BCS-type ground state of the color superconductor is an important concept in the study of this state of matter. One can explore the rich phases of the color superconductor by determining the patterns of spontaneously symmetry breaking. From the Ginzburg-Landau free energy, we classify and study the phases of the spin-one color superconductor. We construct a theoretical framework based on mean field theory in QCD in which we can calculate the fermion spectral density to describe the dynamic behavior of the gapped quarks.The phase transition of color superconductivity is closely related to the spon-taneously symmetry breaking of the system. The direct consequence is the emer-gence of Nambu-Goldstone (NG) bosons. We derive the Ginzburg-Landau free en-ergy for the low energy excitations. The effective Lagrangian can be constructed from the free energy. The dispersion relation of the NG bosons can then be ob-tained. Different patterns of spontaneously symmetry breaking give the different kinematic modes of the NG bosons. Due to non-vanishing conserved charges in the vacuum state of the spin-one color superconductor, we find abnormal excitations different from the traditional NG modes whose dispersion relation is E～|p|2while the traditional one for massless NG bosons is E～|p|. These abnormal ex-citations are called type-Ⅱ NG modes. The hydrodynamics properties of the color superconductor at low temperature is dominated by NG excitions.We construct an effective model for the NG bosons and calculate transport coefficients such as shear viscosity of spin-one color superconductor at low temperatures.Due to the fact that the strange quark mass is large at moderate densities, two-flavor color superconductor should be present in that region of the phase diagram. Since NG bosons are excitations in the system, the fluctuation effects are important. Using the Cornwall-Jaciw-Tomboulis (CJT) formalism, We describe the process in which the effective Cooper pairs at high densities are transformed to the ’real’ diquarks at moderate densities. At the same time, diquarks can also have effects on quarks. Using Hubbard-Stratonovich transformation, we get the fluctuation back to NJL model. We then use Dyson-Schwinger (DS) equation to calculate the spectral density of diquarks and find the existence of type-II NG modes just as we have done from spontaneously symmetry breaking analysis. Quarks also behaves differently with diquarks interaction. By the DS equation, we also calculate the quark spectral density and find that the unpaired quarks have ’pseudo-gap’ due to fluctuation effects. In the region close to the critical temperature, the feature of the pseudo-gap becomes more obvious. We study the non-Fermi-liquid behavior below, close to and above the critical temperature.