The Effects Of Magnetic Field And Chiral Chemical Potential On Phase Transitions In Fermion Systems

In high energy nuclear physics, inspired by the studies on chiral magnetic effect and excited by the anomalous magnetic effect found in Lattice QCD calculations in recent years, the effects of magnetic field and chiral chemical potential in QCD phase transitions are more and more concerned. On one hand, these kinds of researches will promote our understanding of the well-known results; on the other hand, we can get an overall insight of these parameters.Considering the needs of actual research and personal interests, I generally study the effects of magnetic field and chiral chemical potential on chiral restoration, pion superfluidity and color superconductivity. For the studies of charged pion superfluidity and color superconductivity in a magnetic field, we adopt the Ginzburg-Landau approach and the ”rotated” magnetic field method, respectively, to simplify the problems. On the other hand, we systematically discuss the effect of chiral chemical potential on chiral symmetry restoration and the corresponding collective excitation modes in different dimensions, since the discussions of chiral chemical potential are quite preliminary up to now. According to our numerical results, chiral condensate and color condensate both increase with the magnetic field(magnetic catalysis), but it becomes hard for pion superfluid to exist in a magnetic field(inverse magnetic catalysis). However, with increasing chiral chemical potential, chiral condensate, pion condensate and color condensate all increase because they’re all composed of particles(or particle and antiparticle) with the same helicity. Moreover, if magnetic field effect is considered together with chiral chemical potential effect, we would find the interesting d Hv A oscillations. And the d Hv A oscillations not only depend on the kind of phase transitions, but also are related to the space-time dimensions of the systems. In different dimensions, it is found that nonzero chiral condensate is always favored whenever the chiral chemical potential is finite and the attractive coupling constant is non-vanishing, which is very similar to the effect of magnetic field.I also discuss the crystal structure of the order parameter of color superconductor at high density, and the effects of density and magnetic field on topological transitions of2 + 1 dimensional systems. By utilizing ”small block matrix” approximation, we are able to derive the following result quite precisely: The body-centered cubic structure is morefavored around the conventional LO-Normal transition point. As for BCS-BEC topological transition, we use the non-relativistic finite temperature theory and find: The sound velocity of the collective mode corresponds to the second derivative of the thermodynamic potential and can also reflect the characters of the topological transition. The study of Kosterlits-Thouless transition at finite magnetic field is very complicated, but we manage to obtain the explicit expressions of the gap equation and phase stiffness by adopting the Ritus’ s method. The results show that the magnetic field will enhance Kosterlits-Thouless transition temperature alone, but will induce a valley when combined together with chiral chemical potential, which is also the d Hv A oscillation effect.