In this paper, we construct a holographic antiferromagnetism model by introducing two real antisymmetric tensor fields that are coupled to the background gauge field strength and interact with each other within a four-dimensional Gauss-Bonnet gravity background, and investigate the influence of the Gauss-Bonnet coupling constant c on the paramagnetism-antiferromagnetism phase transition. Through numerical shooting method, we discover that a phase transition exists in Gauss-Bonnet black hole under the probe limit. In the absence of an external magnetic field, the increase of value c raises the critical temperature, making the paramagnetism-antiferromagnetism phase transition more likely to occur. When an external magnetic field is present, the magnetic susceptibility follows the Curie-Weiss law with temperature in the paramagnetic phase region, exhibiting a pronounced peak at the critical temperature. Furthermore, the peak value of the susceptibility increases with the increasing of c.

In the probe limit, we investigate the effects of the quartic field strength correction on the holographic paramagnetism-ferromagnetism phase transition in the four-dimensional Gauss-Bonnet gravity background. We find that when the Gauss-Bonnet parameter α is fixed, the presence of the higher correction parameter a in the Maxwell field decreases the critical temperature and makes it harder for condensation to form in the case without an external magnetic field. Furthermore, in the large temperature, the magnetic susceptibility density always satisfies the Curie-Weiss law, and the increase of parameter a will result in a shortening of the period of the external magnetic field.

At the probe level, we investigate the holographic p-wave conductor/superconductor phase transition by both numerical and analytical methods. Especially, due to the nonlinear axion correction, the translational symmetry in superconductor is broken spontaneously. We then study the effects of the axion correction (or disorder) and the mass of vector field on the superconductor phase transition. Concretely, as the disorder parameter and the scaling dimension of vector operator increase, the critical temperature decreases and the stable value of condensate at the low temperature as well as the energy gap increase, which suggests that the larger mass of vector field and the disorder correction inhibit the phase transition, and increase the strength of interaction in superconductor. Near the critical point, the system always undergoes a second-order phase transition, which is independent of the disorder strength and the mass of vector field. According to the behaviors of grand potential and conductivity, the hairy state is verified to be thermodynamical favored and indeed superconducting state. Meanwhile, the analytical results uphold the numerical ones in terms of the critical behavior of condensate.

In this paper, under the background of four-dimensional Gauss-Bonnet gravity, the changes of the critical temperature, the magnetic moment and other physical quantities in the holographic ferromagnetic model with the Gauss-Bonnet coupling α are studied. Calculations show that the critical temperature decreases as the Gauss-Bonnet coupling α increases, and the magnetic moment is more difficult to form when there is no external magnetic field and the temperature is below the critical temperature. After applying an external magnetic field, the variation of the magnetic susceptibility density with the Gauss-Bonnet coupling α in the high temperature region is consistent with the Curie-Weiss law, and in the low temperature region, a single magnetic field-dominated hysteresis loop appears for different Gauss-Bonnet coupling α. And as the Gauss-Bonnet coupling coefficient α increases, the period of the hysteresis loop becomes longer.

Based on the holographic duality, we construct the new p-wave metal/superconductor phase transitions triggered by the electric and magnetic fields. Especially, using the axion field, we introduce simultaneously the spontaneous (SBT) and explicit (EBT) breaking of translation and then investigate how the SBT and EBT corrections influence on the critical temperature, vector condensate and the optical conductivity. Concretely, for the case with pure electric field, both the EBT correction with weak SBT correction and the SBT correction lower the critical temperature Tc and soften the energy gap. Interestingly, for the strong enough SBT correction, the increasing EBT correction enhances firstly and then inhibits the phase transition. Meanwhile, the increasing EBT correction suppresses the SBT effect on Tc. At the lowest Landau energy level, the stronger SBT correction suppresses the phase transition for the weak magnetic field, whose inhibiting effect is finally eliminated by the strong enough magnetic field. The monotonic dependence of Tc on the EBT correction only exists for the weak SBT correction. For the Landau energy level in the excited state, the monotonic dependence of Tc on the EBT correction vanishes for the intermediate SBT correction with large magnetic field.

We invastigate numerically the holographic entanglement entropy (HEE) and holographic subregion complexity (HSC) for a p-wave superconductor with backreaction in the framework of dRGT massive gravity. We calculate the HEE and HSC as functions of subregion strip-width or temperature by following the RT formula and CV conjecture. It is shown that both the HEE and HSC exhibit a discontinuity in their slope at the critical temperature, hence the two physical quantities can be able to probe the p-wave superconducting phase transition. Both the HEE and HSC increase linearly at the large strip-widths, which is consistent with the “area law” of entanglement entropy and the definition of complexity in quantum information. We notice that the HEE in the superconducting phase is always lower than that in the normal phase. In contrast, the behavior of HSC shows a distinct and intriguing dependence on the strip-width. Through comparing the values of HEE and HSC for different massive coupling constants or backreaction, we find that increasing backreaction or introducing massive gravity term results in a notable increase in both HEE and HSC.

Gamma-ray bursts (GRBs) are usually classified into long/short categories according to their durations, but controversy still exists in this aspect. Here we re-examine the long/short classification of GRBs and further compare the cosmological distribution and evolution of each potential subclass. A large number of Swift/BAT GRBs are analyzed in this study. The Gaussian mixture model is used to fit the duration distribution as well as the joint distribution of duration and hardness ratio, and the Akaike and Bayesian information criteria are adopted to assess the goodness of fit. It is found that three Gaussian components can better fit both the univariate and bivariate distributions, indicating that there are three subclasses in the Swift/BAT GRBs, namely short, intermediate, and long subclasses. The non-parametric Efron-Petrosian and Lynden-Bell's c^- methods are used to derive the luminosity function and formation rate from the truncated data of bursts with known redshift in each subclass. It is found that the luminosity distributions and birth rates of the three subclasses are different, further supporting the existence of the intermediate subclass in the Swift/BAT GRBs.

Gamma-ray bursts (GRBs) are usually classified into long/short categories according to their durations, but controversy still exists in this aspect. Here we reexamine the long/short classification of GRBs and further compare the cosmological distribution and evolution of each potential subclass. A large number of Swift Burst Alert Telescope (BAT) GRBs are analyzed in this study. The Gaussian mixture model is used to fit the duration distribution as well as the joint distribution of duration and hardness ratio, and the Akaike and Bayesian information criteria are adopted to assess the goodness of fit. It is found that three Gaussian components can better fit both the univariate and bivariate distributions, indicating that there are three subclasses in the Swift/BAT GRBs, namely, short, intermediate, and long subclasses. The nonparametric Efron-Petrosian and Lynden-Bell's c- methods are used to derive the luminosity function and formation rate from the truncated data of bursts with known redshift in each subclass. It is found that the luminosity distributions and birth rates of the three subclasses are different, further supporting the existence of the intermediate subclass in the Swift/BAT GRBs.

AbstractIn this paper, in the framework of massive gravity, the holographic entanglement entropy (HEE) and holographic subregion complexity (HSC) are numerically investigated by means of the RT formula and the subregion CV conjucture for holographic superconductor with backreaction. We find that both the HEE and HSC exhibit discontinuity of slope at critical temperature, hence both of them are able to reflect the information of phase transition in the holographic superconducting system. Different from the previous studies, the HEE and HSC as function of strip-width are not always lower in the superconducting phase than ones in the normal phase, in particular the HSC decreases linearly as the subregion increases for positive coupling parameters. We notice that when the coupling parameters $$\alpha $$ α and $$\beta $$ β are taken as positive values, the HSC behaves in the same way as HEE, but when they are negative, the HSC has many different behaviors from HEE. Furthermore, we also observe that the HEE and HSC in the superconducting phase illustrate a tendency to converge to the same value as the temperature approaches zero, regardless of the coupling parameters of model. It is worth mentioning that in the massless gravity limit (the coupling parameters $$\alpha =0$$ α = 0 and $$\beta =0$$ β = 0 ), the results given by us are consistent with the case of holographic superconductor with backreaction from Einstein gravity.

We build holographic p-wave conductor(insulator)/superconductor models via the numerical method with a new form of Weyl coupling in five-dimensional Lifshitz gravity, and then investigate how the Weyl coupling parameter γ and the Lifshitz scaling parameter z affect the superconductor models. In the conductor/superconductor model, an increase in the Weyl correction (Lifshitz scaling) enhances (inhibits) the superconductor phase transition. Meanwhile, both the Weyl correction (when the Lifshitz parameter is large enough and fixed) and the Lifshitz scaling suppress the growth of the real part of the conductivity. The Weyl correction used here (CB 2) shows weaker effects on the critical value than the previous Weyl correction (CF 2). In the insulator/superconductor model, larger vaules of the Weyl parameter hinder the formation of condensate. However, in increase in the Lifshitz scaling enhances the appearance of condensate. In addition, the calculation suggests that a competitive relation may exist between the Weyl correction and the Lifshitz scaling.

In the probe limit, we construct the p-wave conductor/superconductor phase transition with momentum relaxation originated from the axion fields by both numerical and analytical methods, and then study the effects of relaxation parameter (k/μ) on the superconductor model. Concretely, the increasing k/μ decreases monotonously the critical temperature and thus hinders the phase transition. The stable value of condensate (C00≡〈Jx〉1/(Δ+1)/μ|T≈0.15Tc) and the coefficient (C1) of condensate (〈Jx〉/μ1/(Δ+1)=C11−T/Tc|T≈Tc) always decrease with the larger k/μ. Near the critical point, the system suffers from a second order phase transition. Meanwhile, for fixed value of k/μ, the larger mass of vector field also suppresses the vector condensate to emerge. As for the above conclusions, the analytical results from the improved trial function agree with the numerical ones. The calculation of the ratio of energy gap to the critical temperature shows that the present superconductor indeed involves strong interaction, which increases with the increasing k/μ.

Based on the dynamics of single scalar field slow-roll inflation and the theory of reheating, we investigate the generalized natural inflationary (GNI) model. Concretely, we give constraints on the scalar spectral index $n_{s}$ and tensor-to scalar ratio $r$ for $\Lambda$CDM $+r$ model according to the latest data from Plack 2018 TT,TE,EE+lowE+lensing (P18) and BICEP2/Keck 2015 season (BK15), i.e., $n_{s}=0.9659\pm0.0044$ at $68\%$ confidence level (CL) and $r<0.0623$ at $95\%$CL. We find that the GNI model is favored by P18 plus BK15 in the ranges of $\log_{10}(f/M_{p})=0.62^{+0.17}_{-0.18}$ and $m=0.35^{+0.13}_{-0.23}$ at $68\%$CL. In addition, the corresponding predictions of the general and two-phase reheating are respectively discussed. It follows that the parameter $m$ has the significant effect on the model behaviors.

Abstract Via numerical and analytical method, we construct the holographic p-wave conductor/superconductor model with $$C^2F^2$$ C2F2 correction (where $$C^2F^2=C_{\mu \nu }^{\alpha \beta }C_{ \alpha \beta }^{\mu \nu }F_{\rho \sigma }F^{\rho \sigma }$$ C2F2=CμναβCαβμνFρσFρσ , and $$C_{\mu \nu }^{\alpha \beta }$$ Cμναβ and $$F_{\rho \sigma }$$ Fρσ denotes the Weyl tensor and gauge field strength, respectively.)in the four-dimensional Schwarzschild-AdS black hole, and mainly study the effects of $$C^2F^2$$ C2F2 correction parameter denoted by $$\gamma $$ γ on the properties of superconductors. The results show that for all values of the $$C^2F^2$$ C2F2 parameter, there always exists a critical temperature below which the vector hair appears. Meanwhile, the critical temperature increases with the improving $$C^2F^2$$ C2F2 parameter $$\gamma $$ γ , which suggests that the improving $$C^2F^2$$ C2F2 parameter enhances the superconductor phase transition. Furthermore, at the critical temperature, the real part of conductivity reproduces respectively a Drude-like peak and an obviously pronounced peak for some value of nonvanishing $$C^2F^2$$ C2F2 parameter. At the low temperature, a clear energy gap can be observed at the intermediate frequency and the ratio of the energy gap to the critical temperature decreases with the increasing $$C^2F^2$$ C2F2 parameter, which is consistent with the effect of the $$C^2F^2$$ C2F2 parameter on the critical temperature. In addition, the analytical results agree well with the numerical results, which means that the analytical Sturm–Liouville method is still reliable in the grand canonical ensemble.

为了深入探讨万有引力的性质,在经典的牛顿万有引力理论基础之上,结合相对论动力学理论与等效原理,对牛顿的万有引力理论进行了适当推广,提出了一种修正的牛顿引力方程,然后利用推广的牛顿万有引力理论推导出行星运动的轨道方程与行星在近日点进动率的一般公式,且以水星近日点进动为例,验证了该推广的合理性.

利用MOJAVE数据库15 GHz的总流量密度变化的监测数据,分析了一个大样本耀变体射电喷流的相对论性束流性质,计算了源的亮温度、多普勒增亮因子、洛伦兹因子、视向角与光变指数等.研究发现,该样本中多数耀变体是多普勒增强的,且平谱射电类星体整体上比蝎虎天体具有更强的多普勒增亮效应.洛伦兹因子与光变指数的计算表明,与平谱射电类星体相比,蝎虎天体有较小的洛伦兹因子和光变指数.通过视向角的计算分析发现,89％的耀变体的视向角小于21?.此外,还分析了耀变体的亮温度与光变指数的关系,发现它们具有较显著的相关性.

In the probe limit, we numerically study the holographic p-wave superconductor phase transition in the high-order derivative theory. Concretely, we study the influences of the high-order derivative correction term αRF2 on the Maxwell complex vector model (MCV) in the five-dimensional AdS black hole and soliton backgrounds, respectively. In the black hole background, the improving correction parameter α increases the critical temperature and thus enhances the conductor/superconductor phase transition. Meanwhile, as the RF2 correction becomes stronger, the ratio of the energy gap to the critical temperature decreases from 9.858 to 5.995, which obviously deviates from the universal value. In the soliton background, we find that the correction does not affect the critical chemical potential. However, as the correction parameter α increases, the vector condensate grows faster, which might suggest that the improving α enhances the insulator/superconductor in some sense. The location of the second pole of imaginary part of conductivity increases with α, which implies that the energy of the quasiparticle excitation increases with the improving correction. In addition, the effects of α on the superfluid density agree with the one on the critical value as well as the condensate in both models. Furthermore, the critical exponent of condensate and superfluid density near the critical point is always 1/2 and 1, respectively.

We numerically realize the holographic s-wave conductor/superconductor model in the four-dimensional Lifshitz black hole with six derivative (SD) correction, and mainly study the influences of the Lifshitz parameter z as well as the SD parameter γ on the superconductor model. The results show that the increasing z inhibits the superconductor phase transition for large enough γ but enhances the phase transition for small enough γ. Meanwhile, the larger γ enhances the superconductor phase transition for small enough z (such as z=1,65), but inhibits the phase transition for large enough z, for example, z=85. Furthermore, for fixed γ, there exists a pronounced peak increasing with the improving z. However, for fixed z, the pronounced peak and the energy gap become weaker and weaker with the increasing γ. In addition, with the increasing z, the energy gap decreases for small enough γ but increases for large enough γ, which agrees well with the phase diagram of the critical temperature.

在探子极限下,通过解析方法研究了超导体相变的磁效应和高阶修正效应.具体来说,我们把带质量的麦克斯韦复矢量场耦合到4维AdS黑洞中,构造了全息p波导体/超导体相变.首先,通过扰动方法得到了表征磁效应的多普勒解,进而对多普勒解叠加得到不同形状的涡流格点.其次,在最低朗道能级下,磁场促进相变,高阶修正抑制相变.在激发态能级下,磁场和高阶修正对超导相变的影响与最低能态下情况相反.并且,解析结果与已有的数值结果定性一致.

In the probe limit, we numerically construct the holographic p-wave superconductor model in the Lifshitz gravity with the high-order derivative correction. Concretely, we study the effects of both Lifshitz scaling and the RF2 correction on the Maxwell-complex-vector model in the five-dimensional Lifshitz black hole and soliton backgrounds, respectively. We find that the increasing Lifshitz parameter u inhibits the conductor/superconductor phase transition and suppresses the frequency dependent conductivity. For the coexistence of both Lifshitz parameter and RF2 correction, the larger Lifshitz parameter u suppresses the effect of RF2 correction on the superconductor model. Moreover, the Lifshitz parameter inhibits the insulator/superconductor phase transition at first, and then enhances the phase transition when the value of Lifshitz parameter is large enough. Meanwhile, the larger parameter u enlarges the energy of quasiparticle excitation. Near the critical point, both systems undergo a second-order phase transition, which is upheld by the comparison of grand potential between normal state and condensate state.

AlN diluted magnetic semiconductor powders (DMSs) with microspheres room temperature (RT) ferromagnetism were successfully synthesized in situ by arc method with high purity Al powder and N2 as reaction materials.X-ray diffraction (XRD) test showed that AlN powder was hexagonal wurtzite structure.Scanning electron microscopy (SEM) showed that the average particle size of AlN powders microsheets was in the range of 2-40 and the average particle size of AlN powders microspheres was in the range of 3-30.AlN powders composition of Al and N was observed by an energy dispersive spectrometer (EDS) and N was insufficient.The Photoluminescence (PL) spectra of AlN powder showed that the luminescence of AlN powder was mainly caused by defects such as N vacancy and intrinsic defects.The vibrating sample magnetometer (VSM) showed that AlN powder exhibited increased ferromagnetism at room temperature,the saturation magnetization and coercivity were 130.0 A/m and 13.68 kA/m,respectively.After annealing at 950 ℃ ammonia atmosphere for 8 h,the saturation magnetization and coercivity were 48.6 A/m and 8.536 kA/m,respectively.We considered that the related defects play an important role to contribute for ferromagnetic order in AlN DMSs powders.