Via numerical and analytical methods, the effects of the Lifshitz dynamical exponent z on the holographic superconductor models are studied in some detail, including s-wave and p-wave models. Working in the probe limit, we calculate the condensation and conductivity in both Lifshitz black hole and soliton backgrounds with a general z. For both the s-wave and p-wave models in the black hole backgrounds, as z increases, the phase transition becomes difficult and the conductivity is suppressed. For the Lifshitz soliton background, when z increases, the critical chemical potential increases in both the s-wave model (with a fixed mass of the scalar field) and p-wave model. For the p-wave model in both the Lifshitz black hole and soliton backgrounds, the anisotropy between the AC conductivity in different spatial directions is suppressed when z increases. In all cases, we find that the critical exponent of the condensation is always 1/2, independent of z and spacetime dimension. The analytical results from the Sturm-Liouville variational method uphold the numerical calculations. The implications of these results are discussed.
In the probe limit, we numerically construct a holographic p-wave superfluid model in the four-dimensional (4D) and five-dimensional (5D) anti-de Sitter black holes coupled to a Maxwellcomplex vector field. We find that, for the condensate with the fixed superfluid velocity, the results are similar to the s-wave cases in both 4D and 5D spacetimes. In particular, the Cave of Winds and the phase transition always being of second order take place in the 5D case. Moreover, we find the translating superfluid velocity from second order to first order increases with the mass squared.Furthermore, for the supercurrent with fixed temperature, the results agree with the GinzburgLandau prediction near the critical temperature. In addition, this complex vector superfluid model is still a generalization of the SU(2) superfluid model, and it also provides a holographic realization of the He 3 superfluid system.
The behaviors of the holographic superconductors/insulator transition are studied by introducing a charged scalar field coupled with a logarithmic electromagnetic field in both the Einstein-Gauss-Bonnet AdS black hole and soliton. For the Einstein-Gauss-Bonnet AdS black hole, we find that: i) the larger coupling parameter of logarithmic electrodynamic field b makes it easier for the scalar hair to be condensated; ii) the ratio of the gap frequency in conductivity ω g to the critical temperature T c depends on both b and the Gauss-Bonnet constant α; and iii) the critical exponents are independent of the b and α. For the Einstein-Gauss-Bonnet AdS Soliton, we show that the system is the insulator phase when the chemical potential µ is small, but there is a phase transition and the AdS soliton reaches the superconductor (or superfluid) phase when µ larger than critical chemical potential. A special property should be noted is that the critical chemical potential is not changed by the coupling parameter b but depends on α.
In this paper, we study the motion of photons around a KehagiasSfetsos (KS) black hole and obtain constraints on IR modified Hořava gravity without cosmological constant (∼ W ). An analytic formula for the light deflection angle is obtained. For a propagating photon, the deflection angle δϕ increases with large values of the Hořava gravity parameter ω. Under the UV limit ω −→ ∞, deflection angle reduces to the result of usual Schwarzschild case, 4G M/R. It is also found that with increasing scale of astronomical observation system the Hořava-Lifshitz gravity should satisfy |ωM 2 | > 1.1725 × 10 −16 with 12% precision for Earth system, |ωM 2 | > 8.27649 × 10 −17 with 17% precision for Jupiter system and |ωM 2 | > 8.27650 × 10 −15 with 0.17% precision for solar system.
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