Modified Friedmann equations from Debye entropic gravity

A remarkable new idea on the origin of gravity was recently proposed by Verlinde who claimed that the laws of gravitation are no longer fundamental, but rather emerge naturally as an entropic force. In Verlinde derivation, the equipartition law of energy on the holographic screen plays a crucial role. However, the equipartition law of energy fails at the very low temperature. Therefore, the formalism of the entropic force should be modified while the temperature of the holographic screen is very low. Considering the Debye entropic gravity and following the strategy of Verlinde, we derive the modified Newton’s law of gravitation and the corresponding Friedmann equations which are valid in all range of temperature. In the limit of strong gravitational field, i.e. high temperature compared to Debye temperature, T » T _D , one recovers the standard Newton’s law and Friedmann equations. We also generalize our study to the entropy corrected area law and derive the dynamical cosmological equations for all range of temperature. Some limits of the obtained results are also studied.     

Temperature and Energy of 4-Dimensional Axisymmetric Black Holes from Entropic Force

We investigate the temperature and energy on holographic screens for 4-dimensional axisymmetric black holes with the entropic force idea proposed by Verlinde. According to the principle of thermal equilibrium, the location of holographic screen outside the axisymmetric black hole horizon is not a equivalent radius surface. The location of isothermal holographic screen outside the axisymmetric black hole horizon is obtained. Using the equipartition rule, we derive the correction expression of energy of isothermal holographic screen. When holographic screens are far away the black hole horizon, the entropic force of charged rotating particles can be expressed as Newton’s law of gravity. When the screen crosses the event horizon, the temperature of the screen agrees with the Hawking temperature and the entropic force gives rise to the surface gravity for both of the black holes.     

Nonhomogeneous Cooling, Entropic Gravity and MOND Theory

In this paper, by using the holographic principle, a modified equipartition theorem where we assume that below a critical temperature the energy is not equally divided on all bits, and the Unruh temperature, we derive MOND theory and a modified Friedmann equation compatible with MOND theory. Furthermore, we rederive a modified Newton’s law of gravitation by employing an adequate redefinition of the numbers of bits.     

Thoughts on entropic gravity in the Parikh–Wilczek tunneling model of Hawking radiation

In this letter, we use the Parikh–Wilczek tunneling model of Hawking radiation to illustrate that a reformulation of Verlinde’s entropic gravity is needed to derive Newton’s law for a temperature-varying screen, required by the conservation of energy. Furthermore, the entropy stored in the holographic screen is shown to be additive and its temperature dependence can be obtained.     

Modified Friedmann Equations on the Brane from Entropic Force

The well-known area relation of the black hole entropy can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. Applying this modified entropy-area relation to brane cosmology, we derive the modified cosmological equations governing the evolution of the universe on the brane. We adopt the viewpoint that interprets gravity as an entropic force caused by the changes in the information when a material body moves away from the holographic screen.     

Time Varying Gravitational Constant G via Entropic Force

If the uncertainty principle applies to the Verlinde entropic idea, it leads to a new term in the Newton's second law of mechanics in the Planck's scale. This curious velocity dependent term inspires a frictional feature of the gravity. In this short letter we address that this new term modifies the effective mass and the Newtonian constant as the time dependentquantities. Thus we must have a running on the value of the effective mass on the particle mass m near the holographic screen and the G. This result has a nigh relation with the Dirac hypothesis about the large numbers hypothesis (L.N.H.). We propose that the corrected entropic terms via Verlinde idea can be brought as a holographic evidence for the authenticity of the Dirac idea.     

Dilatonic Entropic Force

We show in detail that the entropic force of the static spherically symmetric spacetimes with unusual asymptotics can be calculated through the Verlinde’s arguments. We introduce three different holographic screen candidates, which are first employed thoroughly by Myung and Kim [Phys. Rev. D 81, 105012 (2010)] for Schwarzschild black hole solutions, in order to identify the entropic force arising between a charged dilaton black hole and a test particle. The significance of the dilaton parameter on the entropic force is highlighted, and shown graphically.     

Entropic Corrections to Coulomb’s Law

Two well-known quantum corrections to the area law have been introduced in the literatures, namely, logarithmic and power-law corrections. Logarithmic corrections, arises from loop quantum gravity due to thermal equilibrium fluctuations and quantum fluctuations, while, power-law correction appears in dealing with the entanglement of quantum fields in and out the horizon. Inspired by Verlinde’s argument on the entropic force, and assuming the quantum corrected relation for the entropy, we propose the entropic origin for the Coulomb’s law in this note. Also we investigate the Uehling potential as a radiative correction to Coulomb potential in 1-loop order and show that for some value of distance the entropic corrections of the Coulomb’s law is compatible with the vacuum-polarization correction in QED. So, we derive modified Coulomb’s law as well as the entropy corrected Poisson’s equation which governing the evolution of the scalar potential ϕ. Our study further supports the unification of gravity and electromagnetic interactions based on the holographic principle.     

Holographic considerations on a Machian Universe

MOND theory explains the rotation curves of the galaxies. Verlinde’s ideas establish an entropic origin for gravitational forces and Tsallis principle generalizes the theory of Boltzmann–Gibbs. In this work we have promoted a connection between these recent approaches, that at first sight seemed to have few or no points in common, using the Mach’s principle as the background. In this way we have used Tsallis formalism to calculate the main parameters of the Machian Universe including the Hubble parameter and the age of the Universe. After that, we have also obtained a new value for the Tsallis parameter via Mach’s principle. Using Verlinde’s entropic gravity we have obtained new forms for MOND’s well established ingredients. Finally, based on the relations between particles and bits obtained here, we have discussed the idea of bits entanglement in the holographic screen.     

Entropic force, holography and thermodynamics for static space-times

Recently Verlinde has suggested a new approach to gravity which interprets gravitational interaction as a kind of entropic force. The new approach uses the holographic principle by stating that the information is kept on the holographic screens which coincide with equipotential surfaces. Motivated by this new interpretation of gravity (but not being limited by it) we study equipotential surfaces, the Unruh–Verlinde temperature, energy and acceleration for various static space-times: generic spherically symmetric solutions, axially symmetric black holes immersed in a magnetic field, traversable spherically symmetric wormholes of an arbitrary shape function, system of two and more extremely charged black holes in equilibrium. In particular, we have shown that the Unruh–Verlinde temperature of the holographic screen reaches absolute zero on the wormhole throat independently of the particular form of the wormhole solution.     

N型4H-SiC低温拉曼光谱特性

利用拉曼散射技术对N型4H-SiC单晶材料进行了30～300 K温度范围的光谱测量。实验结果表明,随着温度的升高,N型4H-SiC单晶材料的拉曼峰峰位向低波数方向移动,峰宽逐渐增宽。分析认为,晶格振动随着温度的升高而随之加剧,其振动恢复力会逐渐减小,使振动频率降低;原子相对运动会随温度的升高而加剧,使得原子之间及晶胞之间的相互作用减弱,致使声学模和光学模皆出现红移现象。随着温度的升高,峰宽逐渐增宽。这是由于随着温度的升高声子数逐渐增加,增加的声子进一步增加了散射概率,从而降低了声子的平均寿命,而声子的平均寿命与峰宽成反比,因此随着温度的升高峰宽逐渐增宽。声子模强度随温度升高呈现不同规律,E₂(LA),E₂(TA),E₁(TA)和A₁(LA)声子模随着温度升高强度单调增加,而E₂(TO),E₁(TO)和A₁(LO)声子模强度出现了先增后减的明显变化,在138 K强度出现极大值。分析认为造成原因是由于当温度高于138 K时,高能量的声子分裂成多个具有更低能量的声子所致。     

Frequency in Middle of Magnon Band Gap in a Layered Ferromagnetic Superlattice

The frequency in middle of magnon energy band in a five-layer ferromagnetic superlattice is studied by using the linear spin-wave approach and Green's function technique. It is found that four energy gaps and corresponding four frequencie in middle of energy gaps exist in the magnon band along K_x direction perpendicular to the superlattice plane. The spin quantum numbersand the interlayer exchange couplings all affect the four frequencies in middle of the energy gaps. When all interlayer exchange couplings are same, the effect of spin quantum numbers on the frequency ω_g1 in middle of the energy gap Δω₁₂ is complicated, and the frequency ω_g1 depends on the match of spin quantum numbers in each layer. Meanwhile, the frequencies ω_g2, ω_g3, and ω_g4 in middle of other energy gaps increase monotonously with increasing spin quantum numbers. When the spin quantum numbersin each layer are same, the frequencies ω_g1, ω_g2, ω_g3, and ω_g4 all increasemonotonously with increasing interlayer exchange couplings.     

金属氧化物薄膜光学常数计算物理模型应用研究

采用离子束溅射(IBS)方法制备了HfO₂和Ta₂O₅两种金属氧化物薄膜,通过测量薄膜的椭偏参数,使用非线性最小二乘法反演计算获得薄膜的光学常数。 在拟合过程中,采用L₈(27)正交表设计了8组反演计算实验,在初始选定Cauchy模型后,对HfO₂薄膜拟合影响最大的为表面层模型,对Ta₂O₅薄膜拟合影响最大的为折射率梯度模型。 确定了不同物理模型对拟合函数MSE的影响权重和拟合过程中模型选择的次序,按照确定的模型选择次序拟合,最后加入弱吸收模型反演计算两种薄膜的光学常数,反演计算的MSE相对初始MSE可下降79%和39%,表明拟合过程模型选择物理意义明确,具有广泛的应用价值。 在500 nm处,Ta₂O₅薄膜的折射率梯度大于HfO₂薄膜, 而HfO₂薄膜消光系数大于Ta₂O₅薄膜。 表明Hf金属与Ta金属相比容易氧化形成稳定的氧化物,HfO₂薄膜的吸收要高于Ta₂O₅薄膜。     

Squeezing MOND into a Cosmological Scenario

Explaining the effects of dark matter using modified gravitational dynamics (MOND) has for decades been both an intriguing and controversial possibility. By insisting that the gravitational interaction that accounts for the Newtonian force also drives cosmic expansion, one may kinematically identify which cosmologies are compatible with MOND, without explicit reference to the underlying theory so long as the theory obeys Birkhoff's law. We find that the critical acceleration a(0) must have a slight source-mass dependence (a(0) approximately M(1/3)) and that MOND cosmologies are naturally compatible with observed late-time expansion history. However, cosmologies that can produce enough density perturbations to account for structure formation are contrived and fine tuned. Even then, they may be marginally ruled out by evidence of early (z approximately 20) reionization.     

波数线性校正方法在多烯烃和类胡萝卜素Raman光谱频率校正中的应用

采用密度泛函理论计算了两种类胡萝卜素(β-胡萝卜素和叶黄素) 和几种短链(n=2~5)多烯烃的Raman光谱,用波数线性校正(WLS)方法对计算频率进行了校正,并与常用的几种校正方法作了比较。最常用的单一参数校正(UFS)方法只适用于个别频率的校正,对于所有振动频率的综合校正效果并不理想。WLS方法对于多烯烃和类胡萝卜素的校正结果明显优于UFS方法,校正公式分别为ν_obs／ν_calc=0.999 9-0.000 027 4ν_calc和ν_obs／ν_calc=0.993 8-0.000 024 8ν_calc,这些结果说明WLS方法可以用于类胡萝卜素这样的大分子的频率校正。WLS方法对多烯烃和类胡萝卜素的校正参数非常接近,证明WLS方法对多烯烃的校正结果可以用于类胡萝卜素的频率校正,这为类胡萝卜素频率校正提供了一种新的方法。     

疏水表面上吸附态溶菌酶的DSC和FTIR研究

联合差示扫描量热 (DSC)和傅里叶变换红外吸收光谱(FTIR)分别研究了鸡蛋白溶菌酶(Lyz)在适度疏水吸附剂(PEG-600)表面上吸附和折叠时,不同盐(硫酸铵)浓度、表面覆盖度和变性剂(盐酸胍)浓度对无水环境的吸附态天然和变性溶菌酶构象变化及热稳定性的影响。研究发现：随着硫酸铵浓度和溶菌酶表面覆盖度的增加,吸附态天然和变性溶菌酶的吸热峰温度都逐渐降低,同时在较高温度下的微扰也增多。吸附发生后,α-螺旋结构减少,β-折叠和β-转角结构增多。在FTIR图谱中,吸附态变性溶菌酶在1 400～1 425 cm-1处的C—C拉伸振动峰和1 650～1 670 cm-1处的酰胺Ⅰ带特征峰都能明显观测到。但是,与之相比,相同条件下吸附态天然溶菌酶在1 650～1 670 cm-1处特征峰却几乎看不到。吸附态天然溶菌酶发生了结构丢失,表现得更加不稳定。     

Holography, UV/IR Relation, Causal Entropy Bound, and Dark Energy

The constraint on the total energy in a given spatial region is given from holography by the mass of a black hole that just fits in that region, which leads to an UV/IR relation： the maximal energy density in that region is proportional to Mp^2/L^2, where Mp is the Planck mass and L is the spatial scale of that region under consideration. Assuming the maximal black hole in the universe is formed through gravitational collapse of perturbations in the universe, then the ＂Jeans＂ scale of the perturbations gives a causal connection scale RCC. For gravitational perturbations, RCC^-2= Max （H＋ 2H^2, -H） for a fiat universe. We study the cosmological dynamics of the corresponding vacuum energy density by choosing the causal connection scale as the IR cutoff in the UV/IR relation, in the cases of the vacuum energy density as an independently conserved energy component and an effective dynamical cosmological constant, respectively. It turns out that only the case with the choice RCC^-2 = H＋ 2H^2, could be consistent with the current cosmological observations when the vacuum density appears as an independently conserved energy component. In this case, the model is called holographic Ricci scalar dark energy model in the literature.     

非简谐振动对石墨烯杨氏模量与声子频率的影响

在哈里森键联轨道法框架下, 考虑到原子的短程相互作用和原子的非简谐振动, 应用固体物理理论和方法, 得到了石墨烯的力常数、杨氏模量、扭曲模量、泊松系数以及声子频率随温度的变化关系, 探讨了非简谐振动对它们的影响. 结果表明: 1)杨氏模量与声子频率等随温度变化并遵从一定的规律, 其中力常数、杨氏模量、扭曲模量随温度升高而增大, 但变化较小; 声子频率随温度升高而增大但变化较快; 泊松系数随温度升高而较快地减小; 2)石墨烯原子具有沿键长方向的纵振动和垂直键长方向的横振动, 但以纵振动为主, 纵振动的非简谐效应远大于横振动, 横振动的简谐系数ε₀' 和第二非谐系数ε₂' 均小于纵振动的相应值ε₀,ε₂; 比值为ε₀/ε₀' ≈ 8.477,ε₂/ε₂' ≈ 156; 3)若不考虑非简谐振动项, 则石墨烯的力常数、杨氏模量和扭曲模量、泊松系数、声子频率均为常量, 与实验不符合; 同时考虑到原子的第一、二非简谐振动项后, 它们均随温度升高而变化, 而且温度愈高, 原子振动的非简谐效应愈显著. 本文的结果与文献的实验结果符合较好.