Holographic conductivity of holographic superconductors with higher-order corrections

We analytically and numerically disclose the effects of the higher-order correction terms in the gravity and in the gauge field on the properties of s-wave holographic superconductors. On the gravity side, we consider the higher curvature Gauss–Bonnet corrections and on the gauge field side, we add a quadratic correction term to the Maxwell Lagrangian. We show that, for this system, one can still obtain an analytical relation between the critical temperature and the charge density. We also calculate the critical exponent and the condensation value both analytically and numerically. We use a variational method, based on the Sturm–Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. For a fixed value of the Gauss–Bonnet parameter, we observe that the critical temperature decreases with increasing the nonlinearity of the gauge field. This implies that the nonlinear correction term to the Maxwell electrodynamics makes the condensation harder. We also study the holographic conductivity of the system and disclose the effects of the Gauss–Bonnet and nonlinear parameters \(\alpha \) and b on the superconducting gap. We observe that, for various values of \(\alpha \) and b, the real part of the conductivity is proportional to the frequency per temperature, \(\omega /T\), as the frequency is large enough. Besides, the conductivity has a minimum in the imaginary part which is shifted toward greater frequency with decreasing temperature.     

Holographic superconductors in the Born–Infeld electrodynamics

We study the effects of the Born–Infeld electrodynamics on the holographic superconductors in the background of a Schwarzschild–AdS black hole spacetime. We find that the presence of Born–Infeld scale parameter decreases the critical temperature and the ratio of the gap frequency in conductivity to the critical temperature for the condensates. Our results mean that it is harder for the scalar condensation to form in the Born–Infeld electrodynamics.     

Notes on holographic superconductor models with the nonlinear electrodynamics

We investigate systematically the effect of the nonlinear correction to the usual Maxwell electrodynamics on the holographic dual models in the backgrounds of AdS black hole and AdS soliton. Considering three types of typical nonlinear electrodynamics, we observe that in the black hole background the higher nonlinear electrodynamics correction makes the condensation harder to form and changes the expected relation in the gap frequency, which is similar to that caused by the curvature correction. However, in strong contrast to the influence of the curvature correction, we find that in the AdS soliton background the nonlinear electrodynamics correction will not affect the properties of the holographic superconductor and insulator phase transitions, which may be a quite general feature for the s-wave holographic superconductor/insulator system.     

Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics

We show that families of nonlinear gravity theories formulated in a metric-affine approach and coupled to a nonlinear theory of electrodynamics can be mapped into general relativity (GR) coupled to another nonlinear theory of electrodynamics. This allows to generate solutions of the former from those of the latter using purely algebraic transformations. This correspondence is explicitly illustrated with the Eddington-inspired Born–Infeld theory of gravity, for which we consider a family of nonlinear electrodynamics and show that, under the map, preserve their algebraic structure. For the particular case of Maxwell electrodynamics coupled to Born–Infeld gravity we find, via this correspondence, a Born–Infeld-type nonlinear electrodynamics on the GR side. Solving the spherically symmetric electrovacuum case for the latter, we show how the map provides directly the right solutions for the former. This procedure opens a new door to explore astrophysical and cosmological scenarios in nonlinear gravity theories by exploiting the full power of the analytical and numerical methods developed within the framework of GR.     

Analytical Holographic Superconductor with Backreaction Using AdS 3/CFT 2

The holographic model for a two-dimensional superconductor has been investigated by considering the three-dimensional gravity in the bulk. To find the critical temperature, we used the Sturm–Liouville variational method. Where as the same method is applied for calculating the condensation of the dual operators on the boundary. We included the back reactions on the metric by a combination of the perturbation method of the fields with respect to the small parameter and then applying the variational integrals on the resulting equations of the motion. The critical temperature has been successfully obtained on the backreaction effects, and we showed that it dropped with a rise in the backreaction of the fields, and it makes the condensation harder. We can use our analytical results to support the numerical data which was reported previously.     

Critical behaviors of a (2 + 1)-dimensional black hole with a nonlinear electrodynamics source

On the basis of a charged BTZ black hole, we add an extra term in the metric function to describe the contribution from nonlinear electrodynamics. In this way we artificially construct a (2 + 1)-dimensional black hole in general relativity coupled with a nonlinear electrodynamics source. The thermodynamic quantities and Smarr formula are derived. It is found that this black hole has T−S criticality like that of an RN-AdS black hole. Further modifying the metric function, we obtain a (2 + 1)-dimensional black hole possessing P−V critical behaviors similar to that of van der Waals fluid. To our knowledge, this is the first example of (2 + 1)-dimensional black holes having this kind of critical behavior.     

热声现象的一种非线性模型的研究

本文对一种准一维非线性热声模型进行研究,利用该模型初步预测了一种热声驱动器的工作特性,并采用一种更简便的差分格式对系统中发生的非线性现象进行了数值模拟。结果表明,在频域内和线性条件下,该模型简化为经典的线性热声模型,可以预测热声驱动器的起振温度梯度;在时域内和非线性条件下,该模型可以模拟热声系统内的瞬态压力波由初始增长,经过非线性演化,最终达到饱和的全过程;最后,还讨论了板叠上的温度差对饱和压力波的影响。     

拉曼光谱定量分析乙醇含量的非线性回归方法研究

传统拉曼特征峰峰比法一般采用线性回归法建立乙醇浓度与峰峰比的线性关系从而反演乙醇浓度实现乙醇定量分析,但仅在较低浓度范围适用。针对这一问题,采用自主研制的激光拉曼乙醇含量检测系统实验研究了不同浓度乙醇溶液拉曼光谱特征峰(非对称CH₂伸缩振动2 924.0 cm-1)与本底水峰(3 350 cm-1)相对强度关系,提出适用于大范围乙醇浓度测量的非线性回归分析方法。利用邻域平均算法去除拉曼光谱突变噪声,结合多点插值处理实现光谱基线校准。基线校准及归一化处理后,可有效消除突变噪声及强荧光背景的影响。分别采用二次多项式和e指数数学模型对拉曼峰值强度比随乙醇浓度变化关系进行非线性回归并与线性回归分析进行对比。结果表明,线性拟合相关系数约为0.991,线性回归模型乙醇浓度准确测量的适用范围为15%～60%;非线性拟合相关系数高于0.997,非线性回归模型乙醇浓度精确测量的适用范围为3%～97%。非线性数学模型可为乙醇溶液浓度定量分析提供理论基础,将该数学模型应用于乙醇含量检测系统,可实时反演较为精确的乙醇浓度,从而实现大浓度范围内具有荧光背景干扰的乙醇溶液快速、实时、准确的定量分析。     

低维玻色－爱因斯坦凝聚的转变温度和基态占据数

研究了体系中粒子的第一激发态能量对低维玻色凝聚温度的影响,以及不同维度的空间中凝聚温度随总粒子数的变化关系.结果表明,随着粒子敷密度的增加,低维的凝聚温度比高维情形上升得快,体系的凝聚温度与第一激发态能量密切相关.同时计算表明,对于囚禁在GaAs量子阱中的激子气体,即使在无谐振势或幂指数等特殊外势的条件下,也可以在几个K0实现玻色-爱因斯坦凝聚.     

Critical temperature and condensed fraction of Bose-Einstein condensation in optical lattices

Critical temperature and condensate fraction of Bose-Einstein condensation in the optical lattice are studied. The results show that the critical temperature in optical lattices can be characterized with an equivalent critical temperature in a single lattice, which provide a fast evaluation of critical temperature and condensate fraction of Bose-Einstein condensation confined with pure optical trap. Critical temperature can be estimated with an equivalent critical temperature. It is predicted that critical temperature is proportional to q in q number lattices for superfluid state and should be equal to that in a single lattic for Mott insulate state. Required potential depth or Rabi frequency and maximum atom number in the lattices both for superfluid state and Mott state are presented based on views of thermal mechanical statistics.     

Theory of adiabatic variation of critical temperature of the Bose-Einstein condensation of an ideal gas in optical lattice

We calculate the critical temperature of the Bose-Einstein condensation of an ideal Bosegas in the presence of an external periodic potential in one, two, or three directions. A number of assumed approximations enables us to show that the only parameter determining the critical temperature of condensation is the width of the lower energy band with the direct proportionality to the one-third power of this width for each direction of periodicity of the external potential. This also proves the result, obtained earlier by means of numerical calculation, that deepening of the periodic potential (which is known to lead to narrowing of energy bands) leads to lowering of the critical temperature. The fundamental role of quantum tunneling in establishing this regularity is emphasized.     

Holographic Insulator/Superconductor Phase Transition in Born-Infeld Electrodynamics

We study holographic insulator/superconductor phase transition in the framework of Born-Infeld electrodynamics both numerically and analytically. First we numerically study the effects of the Born-Infeld electrodynamics on the phase transition, find that when the Born-Infeld parameter increases, the critical chemical potential keeps invariant but the gap frequency becomes larger. Then we employ the variational method for the Sturm-Liouville eigenvalue problem to study the phase transition analytically. The analytical results obtained are found to be consistent with the numerical results.     

Water condensation kinetics on a hydrophobic surface

Employing thermal desorption spectroscopy, we show that the effective probability of water condensation at low water vapor pressure on an octane film is much below unity at 100-120 K. This unusual finding is related to a small binding energy of H2O monomers on octane (approximately equal to 0.08 eV), requiring the formation of critical water clusters for condensation to occur. This results in strong temperature and impingement-rate dependencies of the water condensation rate and a nonlinear uptake as a function of dose time. All these features are rationalized quantitatively by a kinetic model of water condensation.     

ELECTRODYNAMICS OF A QUASI-(1+1)DIMENSIONAL ELECTRON GAS

A hydrodynamic model. is used to study the electrodynamics of a quasi-(1+1)-dimensional electron gas arranged in a periodic array and neutralized by rigid inert positive background The theory is applied to discuss a new model of quasi-(1+1)-dimensional electron gas with a complex unit cell and an analytical expression of the dispersion relation for this system is derived. The results are the same as. those der-ived caith the semi-classical theory dealing with collective excitations.     

Effect of nonlinear electrodynamics on shadows of slowly rotating black holes

In this study, we investigate the effect of nonlinear electrodynamics on the shadows of charged, slowly rotating black holes with the presence of a cosmological constant. Rather than the null geodesic of the background black hole spacetime, the trajectory of a photon, as a perturbation of the nonlinear electrodynamic field, is governed by an effective metric. The latter can be derived by analyzing the propagation of a discontinuity of the electromagnetic waveform. Subsequently, the image of the black hole and its shadow can be evaluated using the backward ray-tracing technique. We explore the properties of the resultant black hole shadows of two different scenarios of nonlinear electrodynamics, namely, the logarithmic and exponential forms. In particular, the effects of nonlinear electrodynamics on the optical image are investigated, as well as the image's dependence on other metric parameters, such as the black hole spin and charge. The resulting black hole image and shadow display rich features that potentially lead to observational implications.     

用于ITER的NbTi超导股线临界电流测试方法

介绍了一种用于ITER的NbTi超导股线在不同温度下临界电流测试的方法和装置。该装置包括一孔径为70mm、最高磁场高达16T的背景磁体以及变温杜瓦等系统。对NbTi超导线变温测试设计了二元电流引线。用该系统得到了其NbTi超导股线在不同磁场不同温度下的临界电流,用“Luca”定标律拟合了测试结果,并对测试结果进行了分析。     

势场中玻色-爱因斯坦凝聚的临界温度

给出了不同于文献的势场中玻色-爱因斯坦凝聚临界温度表达式.结果揭示了势场中理想玻色子气体凝聚的临界温度与势场之间的关系，表明势场中临界温度正比于无势场情况下临界温度T０ｃ，还给出了势场的有效性判据.势场的有效性是势场与玻尔兹曼常数k和无势场情况下临界温度Ｔ０ｃ乘积ｋＴ０ｃ的比较.当势场接近或大于ｋＴ０c时，临界温度会有效增加;当势场远小于ｋＴ０c时, 势场是无效的. 关键词： 玻色-爱因斯坦凝聚 临界温度 势阱     

Temperature Dependence of In-plane Resistivity and Inverse Hall Angle in NLED Holographic Model

In the strange metal phase of the high-Tc cuprates, it is challenging to explain the linear temperature dependence of the in-plane resistivity and the quadratic temperature dependence of the inverse Hall angle. In this paper, we investigate the temperature dependence of the in-plane resistivity and inverse Hall angle in the nonlinear electrodynamics holographic model developed in our recent work. Maxwell electrodynamics and Born-Infeld electrodynamics are considered. Both cases support a wide spectrum of temperature scalings in parameter space. For Maxwell electrodynamics, the T-linear in-plane resistivity generally dominates at low temperatures and survives into higher temperatures in a narrow strip-like manner. Meanwhile, the T-quadratic inverse Hall angle dominates at high temperatures and extends down to lower temperatures. The overlap between the T-linear in-plane resistivity and the T-quadratic inverse Hall angle, if occurs, would generally present in the intermediate temperate regime. The Born-Infeld case with a 0 is quite similar to the Maxwell case. For the Born-Infeld case with a 0, there can be a constraint on the charge density and magnetic field. Moreover, the overlap can occur for strong charge density.     

Ground State and Single Vortex for Bose-Einstein Condensates in Anisotropic Traps

For Bose-Einstein condensation of neutral atoms in anisotropic traps at zero temperature, we present simple analytical methods for computing the properties of ground state and single vortex of Bose-Einstein condensates, and compare those results to extensive numerical simulations. The critical angular velocity for production of vortices is calculated for both positive and negative scattering lengths a, and find an analytical expression for the large-N limit of the vortex critical angular velocity for a 〉0, and the critical number for condensate population approaches the point of collapse for a 〈 0, by using approximate variational method.     

简谐势阱中非理想气体玻色-爱因斯坦凝聚转变温度的数值研究

用数值计算的方法研究了简谐势阱中非理想气体的玻色 爱因斯坦凝聚情况.通过计算能级的分布，用图形的方式给出了考虑相互作用时，简谐势阱中体系转变温度相对无相互作用体系转变温度的变化趋势 对于存在排斥作用的体系，转变温度升高；对于存在吸引作用的体系，转变温度降低. 关键词： 玻色－爱因斯坦凝聚 相互作用 能级 转变温度