Neutral Color Superconductivity Including Inhomogeneous Phases at Finite Temperature

We investigate neutral quark matter with homogeneous and inhomogeneous color condensates at finite temperature in the frame of an extended NJL model. By calculating the Meissner masses squared and gap susceptibility, the uniform color superconductor is stable only in a temperature window close to the critical temperature and becomes unstable against LOFF phase, mixed phase and gluonic phase at low temperatures. The introduction of the inhomogeneous phases leads to disappearance of the strange intermediate temperature 2SC/g2SC and changes the phase diagram of neutral dense quark matter significantly.Comment: 12 pages, 7 figures. v2: references added, accepted for publication in PRD. V3: Calculation of the neutral LOFF state clarified, typos corrected

Effect of UA(1)U_A(1) Breaking on Chiral Phase Structure and Pion Superfluidity at Finite Isospin Chemical Potential

We investigate the isospin chemical potential effect in the frame of SU(2) Nambu-Jona-Lasinio model. When the isospin chemical potential is less than the vacuum pion mass, the phase structure with two chiral phase transition lines does not happen due to $U_A(1)$ breaking of QCD. When the isospin chemical potential is larger than the vacuum pion mass, the ground state of the system is a Bose-Einstein condensate of charged pions.Comment: Talk presented at Conference on Non-Perturbative Quantum Field Theory: Lattice and Beyond, Guangzhou, China, Dec.16--18, 2004; v2: error correcte

Birkhoff Normal Form and Twist Coefficients of Periodic Orbits of Billiards

In this paper we study the Birkhoff Normal Form around elliptic periodic points for a variety of dynamical billiards. We give an explicit construction of the Birkhoff transformation and obtain explicit formulas for the first two twist coefficients in terms of the geometric parameters of the billiard table. As an application, we obtain characterizations of the nonlinear stability and local analytic integrability of the billiards around the elliptic periodic points.Comment: Revision according to referees' report

Homoclinic and heteroclinic intersections for lemon billiards

We study the dynamical billiards on a symmetric lemon table $\mathcal{Q}(b)$, where $\mathcal{Q}(b)$ is the intersection of two unit disks with center distance $b$. We show that there exists $\delta_0>0$ such that for all $b\in(1.5, 1.5+\delta_0)$ (except possibly a discrete subset), the billiard map $F_b$ on the lemon table $\mathcal{Q}(b)$ admits crossing homoclinic and heteroclinic intersections. In particular, such lemon billiards have positive topological entropy.Comment: Final version. To appear on the journal Advances in Mathematic