Holographic p-wave superconductor models with Weyl corrections

We study the effect of the Weyl corrections on the holographic p-wave dual models in the backgrounds of AdS soliton and AdS black hole via a Maxwell complex vector field model by using the numerical and analytical methods. We find that, in the soliton background, the Weyl corrections do not influence the properties of the holographic p-wave insulator/superconductor phase transition, which is different from that of the Yang-Mills theory. However, in the black hole background, we observe that similar to the Weyl correction effects in the Yang-Mills theory, the higher Weyl corrections make it easier for the p-wave metal/superconductor phase transition to be triggered, which shows that these two p-wave models with Weyl corrections share some similar features for the condensation of the vector operator.Comment: 17 pages, 3 figures, 3 tables, accepted for publication in Phys. Lett.

Holographic insulator/superconductor phase transition with Weyl corrections

We analytically investigate the phase transition between the holographic insulator and superconductor with Weyl corrections by using the variational method for the Sturm-Liouville eigenvalue problem. We find that similar to the curvature corrections, in p-wave model, the higher Weyl couplings make the insulator/superconductor phase transition harder to occur. However, in s-wave case the Weyl corrections do not influence the critical chemical potential, which is in contrast to the effect caused by the curvature corrections. Moreover, we observe that the Weyl corrections will not affect the critical phenomena and the critical exponent of the system always takes the mean-field value in both models. Our analytic results are found to be in good agreement with the numerical findings.Comment: 17 pages, 3 figures and 2 tables. More discussions and references adde

Condensation for non-relativistic matter in Ho\v{r}ava-Lifshitz gravity

We study condensation for non-relativistic matter in a Ho\v{r}ava-Lifshitz black hole without the condition of the detailed balance. We show that, for the fixed non-relativistic parameter $\alpha_2$ (or the detailed balance parameter $\epsilon$), it is easier for the scalar hair to form as the parameter $\epsilon$ (or $\alpha_2$) becomes larger, but the condensation is not affected by the non-relativistic parameter $\beta_2$. We also find that the ratio of the gap frequency in conductivity to the critical temperature decreases with the increase of $\epsilon$ and $\alpha_2$, but increases with the increase of $\beta_2$. The ratio can reduce to the Horowitz-Roberts relation $\omega_g/T_c\approx 8$ obtained in the Einstein gravity and Cai's result $\omega_g/T_c\approx 13$ found in a Ho\v{r}ava-Lifshitz gravity with the condition of the detailed balance for the relativistic matter. Especially, we note that the ratio can arrive at the value of the BCS theory $\omega_g/T_c\approx 3.5$ by taking proper values of $\epsilon$, $\alpha_2$, $\beta_2$ and $m$.Comment: 16 pages, 5 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1001.1472; and text overlap with arXiv:0911.4867 by other author

The Laplacian Eigenvalues and Invariants of Graphs

In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence of Hamiltonicity in a graph involving its Laplacian eigenvalues.Comment: 10 pages,Filomat, 201