Locate QCD Critical End Point in a Continuum Model Study

With a modified chemical potential dependent effective model for the gluon propagator, we try to locate the critical end point (CEP) of strongly interacting matter in the framework of Dyson-Schwinger equations (DSE). Beyond the chiral limit, we find that Nambu solution and Wigner solution could coexist in some area. Using the CornwallJackiw-Tomboulis (CJT) effective action, we show that these two phases are connected by a first order phase transition. We then locate CEP as the end point of the first order phase transition line. Meanwhile, based on CJT effective action, we give a direct calculation for the chiral susceptibility and thereby study the crossover.Comment: 9 pages, 7 figures; Version published in JHE

Characteristic length of a Holographic Superconductor with dd-wave gap

After the discovery of the $s$-wave and $p$-wave holographic superconductors, holographic models of $d$-wave superconductor have also been constructed recently. We study analytically the perturbation of the dual gravity theory to calculate the superconducting coherence length $\xi$ of the $d$-wave holographic superconductor near the superconducting phase transition point. The superconducting coherence length $\xi$ divergents as $(1-T/T_c)^{-1/2}$ near the critical temperature $T_c$. We also obtain the magnetic penetration depth $\lambda\propto(T_c-T)^{-1/2}$ by adding a small external homogeneous magnetic field. The results agree with the $s$-wave and $p$-wave models, which are also the same as the Ginzburg-Landau theory.Comment: last version, 10 pages, accepted by PR

Geometric effects of a quarter of corrugated torus

In the spirit of the thin-layer quantization scheme, we give the effective Shr\"{o}dinger equation for a particle confined to a corrugated torus, in which the geometric potential is substantially changed by corrugation. We find the attractive wells reconstructed by the corrugation not being at identical depths, which is strikingly different from that of a corrugated nanotube, especially in the inner side of the torus. By numerically calculating the transmission probability, we find that the resonant tunneling peaks and the transmission gaps are merged and broadened by the corrugation of the inner side of torus. These results show that the quarter corrugated torus can be used not only to connect two tubes with different radiuses in different directions, but also to filter the particles with particular incident~energies.Comment: 7 pages, 8 figure

The Wigner solution of quark gap equation at nonzero current quark mass and partial restoration of chiral symmetry at finite chemical potential

According to the generally accepted phase diagram of QCD, at low temperature and high baryon number density the chiral phase transition of QCD is of first order and the co-existence of the Nambu-Goldstone phase and the Wigner phase should appear. This is in conflict with the usual claim that the quark gap equation has no Wigner solution in the case of nonzero current quark mass. In this paper we analyze the reason why the Wigner solution does not exist in the usual treatment and try to propose a new approach to discuss this question. As a first step, we adopt a modified Nambu-Jona-Lasinio (NJL) model to study the Wigner solution at finite current quark mass. We then generalize this approach to the case of finite chemical potential and discuss partial restoration of chiral symmetry at finite chemical potential and compare our results with those in the normal NJL model.Comment: 7 pages, 5 figures, and 1 table, discussion at finite chemical potential adde