Phase Structure of Color Superconductivity

We investigate color superconductivity and chiral symmetry restoration at finite temperature and baryon density in the frame of standard two flavor Nambu--Jona-Lasinio model. We derive the diquark mass in RPA, discuss its constraint on the coupling constant in the diquark channel, and find a strong competition between the two phase transitions when the coupling constant is large enough.Comment: Talk presented at Conference on Non-Perturbative Quantum Field Theory: Lattice and Beyond, Guangzhou, China, Dec.16--18, 200

Nucleon Mass Splitting at Finite Isospin Chemical Potential

We investigate nucleon mass splitting at finite isospin chemical potential in the frame of two flavor Nambu--Jona-Lasinio model. It is analytically proved that, in the phase with explicit isospin symmetry breaking the proton mass decreases and the neutron mass increases linearly in the isospin chemical potential.Comment: 3 pages and no figure

Navigation in a small world with local information

It is commonly known that there exist short paths between vertices in a network showing the small-world effect. Yet vertices, for example, the individuals living in society, usually are not able to find the shortest paths, due to the very serious limit of information. To theoretically study this issue, here the navigation process of launching messages toward designated targets is investigated on a variant of the one-dimensional small-world network (SWN). In the network structure considered, the probability of a shortcut falling between a pair of nodes is proportional to $r^{-\alpha}$, where $r$ is the lattice distance between the nodes. When $\alpha =0$, it reduces to the SWN model with random shortcuts. The system shows the dynamic small-world (SW) effect, which is different from the well-studied static SW effect. We study the effective network diameter, the path length as a function of the lattice distance, and the dynamics. They are controlled by multiple parameters, and we use data collapse to show that the parameters are correlated. The central finding is that, in the one-dimensional network studied, the dynamic SW effect exists for $0\leq \alpha \leq 2$. For each given value of $\alpha$ in this region, the point that the dynamic SW effect arises is $ML^{\prime}\sim 1$, where $M$ is the number of useful shortcuts and $L^{\prime}$ is the average reduced (effective) length of them.Comment: 10 pages, 5 figures, accepted for publication in Physical Review

Low-momentum Pion Enhancement Induced by Chiral Symmetry Restoration

The thermal and nonthermal pion production by sigma decay and its relation with chiral symmetry restoration in a hot and dense matter are investigated. The nonthermal decay into pions of sigma mesons which are popularly produced in chiral symmetric phase leads to a low-momentum pion enhancement as a possible signature of chiral phase transition at finite temperature and density.Comment: 3 pages, 2 figure

Exact Calculation of Ring Diagrams and the Off-shell Effect on the Equation of State

The partition function with ring diagrams at finite temperature is exactly caluclated by using contour integrals in the complex energy plane. It contains a pole part with temperature and momentum dependent mass and a phase shift part induced by off-shell effect in hot medium. The thermodynamic potentials for $\phi^4$ and $\phi^3$ interactions are calculated and compared with the quasi-particle (pole) approximation. It is found that the off-shell effect on the equation of state is remarkable.Comment: 7 pages, 11 figures, refereces added, final version to appear in PR

Mott Insulator - Superfluid Transitions in a Two Band Model at Finite Temperature and Possible Application to Supersolid 4He

We study Mott insulator - superfluid transition in a two-band boson Hubbard model, which can be mapped onto a spin-1/2 XY model with spins coupled to an additional Ising degree of freedom. By using a modified mean field theory that include the effects of phase fluctuations, we show that the transition is first order at both zero and finite temperatures. On the Mott insulator side, there may be reentrance in phase transition. These features are consequences of the underlying transition between competing defect poor and defect rich phases. The relevance of the model and our results to supersolid 4He and cold bosonic atoms in optical lattices are discussed