On the Origin of Spacetime Distribution of Quasars II. The Modified Model

The theory of quasar production in collisions of massive black holes with galaxies is developed. The distribution of number of quasars N with respect to the cosmological redshift Z is calculated and a fair agreement with observational data is obtained. The predictive power of the theory to explain a set of observational effects is discussed.     

Peculiar acceleration

It has been proposed recently to observe the change in cosmological redshift of distant galaxies or quasars with the next generation of large telescope and ultra-stable spectrographs (the so-called Sandage–Loeb test). Here we investigate the possibility of observing the change in peculiar velocity in nearby clusters and galaxies. This “peculiar acceleration” could help reconstructing the gravitational potential without assuming virialization. We show that the expected effect is of the same order of magnitude of the cosmological velocity shift. Finally, we discuss how to convert the theoretical predictions into quantities directly related to observations.     

Constraints on unified models for dark matter and dark energy using <Emphasis Type="Italic">H</Emphasis>(<Emphasis Type="Italic">z</Emphasis>)

The differential age data of astrophysical objects that have evolved passively during the history of the universe (e.g. red galaxies) allows us to test theoretical cosmological models through the predicted Hubble function expressed in terms of the redshift z, H(z). We use the observational data for H(z) to test unified scenarios for dark matter and dark energy. Specifically, we focus our analysis on the Generalized Chaplygin Gas (GCG) and the viscous fluid (VF) models. For the GCG model, it is shown that the unified scenario for dark energy and dark matter requires some priors. For the VF model we obtain estimations for the free parameters, which may be compared with further analysis mainly at perturbative level.     

A New Class of Bianchi Cosmological Models in Lyra’s Geometry

The new class of cosmological model of the early Universe filled with perfect fluid in Lyra’s geometry has been considered. We obtain two classes of exact solutions of the field equations in Lyra’s geometry with a time-dependent displacement vector. The exact solutions to the corresponding field equations are obtained in quadrature form. The cosmological parameters have been discussed in detail and it is also shown that the solutions tend asymptotically to isotropic Friedmann-Robertson-Walker cosmological model. We have also discussed the well-known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance d _L and distance modulus μ(z) with redshift.     

五维大反弹宇宙学模型的重建及其相关宇宙学量的演化

在五维大反弹宇宙学模型框架下,通过给定三种不同的暗能量有效态方程,确定了在该模型中起重要作用的函数f(z),从而描述了五维大反弹模型中相关的宇宙学量随红移量z的演化.研究表明,与情形Ⅰ中有效态方程相对应的宇宙学量的演化规律和当前天文观测数据符合最好. 关键词： 大反弹宇宙学模型 暗能量 态方程     

Redshift drift constraints on holographic dark energy

The Sandage-Loeb(SL) test is a promising method for probing dark energy because it measures the redshift drift in the spectra of Lyman-α forest of distant quasars, covering the "redshift desert" of 2 z 5, which is not covered by existing cosmological observations. Therefore, it could provide an important supplement to current cosmological observations. In this paper, we explore the impact of SL test on the precision of cosmological constraints for two typical holographic dark energy models, i.e., the original holographic dark energy(HDE) model and the Ricci holographic dark energy(RDE) model. To avoid data inconsistency, we use the best-fit models based on current combined observational data as the fiducial models to simulate 30 mock SL test data. The results show that SL test can effectively break the existing strong degeneracy between the present-day matter density ?_(m0) and the Hubble constant H0 in other cosmological observations. For the considered two typical dark energy models, not only can a30-year observation of SL test improve the constraint precision of ?_(m0) and h dramatically, but can also enhance the constraint precision of the model parameters c and α significantly.     

Photon distribution functions of fluorescence photons from single nanoparticles: Three different photon counting methods

Mathematical expressions are derived for three photon distribution functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) corresponding to three different methods for counting fluorescence photons from a single nanoparticle excited by continuous laser radiation. Each of the three functions is expressed in terms of Poisson functions, which makes it possible to pass in the w _N ^M (T), w _N ^Z (T), and w _N ^O functions from N multiple integrals to single or double integrals. This not only eases the numerical calculation of the photon distribution, but it also makes it possible to find that, for each exponential process in the dynamics of a nanoparticle, there is a Poisson function in the photon distribution function. All three photon counting methods yield the same photon distribution for continuous fluorescence and different photon distributions for blinking fluorescence.     

The Z = 82 shell closure in neutron-deficient Pb isotopes

Recent mass measurements show a substantial weakening of the binding-energy difference δ_2p(Z, N) = E(Z - 2, N) - 2E(Z, N) + E(Z + 2, N) in the neutron-deficient Pb isotopes. As δ_2p is often attributed to the size of the proton magic gap, it might be speculated that reduction in δ_2p is related to a weakening of the spherical Z = 82 shell. We demonstrate that the observed trend is described quantitatively by self-consistent mean-field models in terms of deformed ground states of Hg and Po isotopes. Received: 25 October 2001 / Accepted: 28 February 2002     

第Ⅰ种强度不对称三态叠加多模叠加态光场N次方Y压缩—第一正交相位分量的压缩情况

根据量子力学中的线性叠加原理,构造了由三个强度不等的多模相干态光场|{Z_j^(A)}>_q、|{Z_j^(B)}>_q和|{Z_j^(C)}>_q的线性叠加所组成的第Ⅰ种强度不对称三态叠加多模叠加态光场|ψ_l^(ABC)>_q.利用多模压缩态理论,研究了态|ψ_l^(ABC)>_q的第一正交方分量(即磁场分量)的广义非线性等幂次N次方Y压缩特性.结果发现:①在上述各多模相干态光场中各模的强度和各模的初始相位各不相等的情况下,态|ψ_l^(ABC)>_q的第一正交分量-磁场分量在一定的条件下,总可呈现出周期性变化的、任意等幂次的N次方Y压缩效应;②当上述各多模相干态光场的强度和各模的初始相位相等时,态|ψ_l^(ABC)>_q的磁场分量的N次方Y压缩现象消失,态|ψ_l^(ABC)>_q可恒处于等幂次N-Y最小测不准态.     

Fluctuation of inverse compressibility for electronic systems with random capacitive matrices

Abstract

This article is concerned with the statistics of the addition spectra of certain many-body systems of identical particles. In the first part, the pertinent system consists of N identical particles distributed among K<N independent subsystems, such that the energy of each subsystem is a quadratic function of the number of particles residing on it with random coefficients. On a large scale, the ground-state energy E(N) of the whole system grows quadratically with N, but in general there is no simple relation such as E_N = aN+bN ². The deviation of E(N) from exact quadratic behaviour implies that its second difference (the inverse compressibility) X_N ≡E(N+1)?2E(N)+E(N?1) is a fluctuating quantity. Regarding the numbers X_N as values assumed by a certain random variable X, we obtain a closed-form expression for its distribution F _(X). Its main feature is that the corresponding density P _(X)=dF _(X)/d _X has a maximum at the point X=0. As K→∞ the density is Poissonian, namely, P(X)→e^?X

This result serves as a starting point for the second part, in which coupling between subsystems is included. More generally, a classical model is suggested in order to study fluctuations of Coulomb blockade peak spacings in large two-dimensional semiconductor quantum dots. It is based on the electrostatics of several electron islands among which there are random inductive and capacitive couplings. Each island can accommodate electrons on quantum orbitals whose energy depends also on an external magnetic field. In contrast to a single-island quantum dot, where the spacing distribution between conductance peaks is close to Gaussian, here the distribution has a peak at small spacing value. The fluctuations are mainly due to charging effects. The model can explain the occasional occurrence of couples or even triples of closely spaced Coulomb blockade peaks, as well as the qualitative behaviour of peak positions with the applied magnetic field.     

Chemical Evolution of the Universe and its Consequences for Gravitational-Wave Astrophysics

Gravitational waves (GW) emitted by merging black holes (BH) and neutron stars are now routinely detected. Those are the afterlives of massive stars that formed all across the Universe—at different cosmic times and with different metallicities. Birth metallicity plays an important role in the evolution of massive stars. Consequently, the population properties of mergers are sensitive to the metallicity dependent cosmic star formation history (f_SFR(Z,z)). In particular, within the isolated formation scenarios (the focus of this paper), a strong low metallicity preference of the formation of BH mergers is found. The origin of this dependence and its consequences are discussed. Most importantly, uncertainty in the f_SFR(Z,z) (substantial even at low redshifts) cannot be ignored in the models. This poses a challenge for the interpretation of the observed GW source population properties. Possible improvements and the role of future GW detectors are considered. Recent efforts to determine f_SFR(Z,z) and the factors that dominate its uncertainty are summarized. Many of those factors stem from the uncertain properties of faint and distant galaxies. The fact that they leave imprint on the redshift-dependent properties of mergers makes GW a promising (and complementary to electromagnetic observations) tool to study galaxy chemical evolution.     

第I种非对称三态叠加多模叠加态光场的高次和压缩——第一正交分量的N次方H压缩效应

构造了第孙中禹种强度不等的非对称三态叠加多模叠加态光场|ψ₁^(ABC)〉_q.利用多模压缩态理论研究了态|ψ₁^(ABC)〉_q第一正交分量高次和压缩.结果发现:①当构成态|ψ₁^(ABC)〉_q的三个多模相干态光场的强度不相等时,在一定条件下,态|ψ₁^(ABC)〉_q的第一正交分量可出现任意幂次的高次和压缩.②当上述的三个多模相干态光场强度相等时,态|ψ₁^(ABC)〉_q的第一正交分量的高次和压缩现象消失.在这种情况下,态|ψ₁^(ABC)〉_q的第一正交分量恒处于NH最小测不准态.     

Feldgleichungen der TREDERschen Gravitationstheorie,die aus einem Variationsprinzip ableitbar sind. I

In the frame work of TREDER 's gravitational theory we consider two classes of field equations which are derivable from two classes of LAGRANGE ian densities Ω⁽¹⁾(ω₁, ω₂), Ω⁽²⁾(s?₁, s?₂). ω₁, ω₂; s?₁, s?₂ are parameters. Ω⁽²⁾(ω₁, ω₂) gives us field equations which are up to the post-NEWTON ian approximation in the sense of NORDTVEDT , THORNE and WILL equivalent to the field equations given by BRANS and DICKE . For ω₂ = ?1 ?2ω₁ field equations follow from Ω⁽¹⁾(ω₁, ?1 ?2ω₁) which are in the above mentioned sense of post-NEWTON ian approximation equivalent to EINSTEIN 's equations. The field equations following from Ω⁽¹⁾(ω₁, ω₂) have a cosmological model with the well known cosmological singularities for T → ± ∞ in case that ω₁/(1 +3ω₁ +ω₂) ? γ > 0. For ω₁/(1 +3ω₁ +ω₂) ≤ 0 cosmological models with no cosmological singularities exist. From Ω⁽²⁾(s?₁, s?₂) we obtain field equations which at the best give us perihelion rotation 7% above EINSTEIN 's value and light deflection 7% below the corresponding EINSTEIN 's value. But in that case we are able to show the existence of a cosmological model without any cosmological singularity.     

Relativistic star clusters with high central redshift

Collisionless star clusters in dynamical equilibrium are of current interest in general relativity and astrophysics. A step-function distribution is chosen for star clusters. The corresponding equation of state is analogous to a Fermi-gas equation. These clusters are found to be pulsationally unstable for a central redshift ofZ _c ⩾ 0·54. Further, a model of clusters is developed in which the core has an extremely relativistic equation of state. These structures are unstable forZ _c ⩾ 2·55 when we use Chandrasekhar’s technique to study their pulsational stability.     

The case for the cosmological constant

I present a short overview of current observational results and theoretical models for a cosmological constant. The main motivation for invoking a small cosmological constant (or A-term) at the present epoch has to do with observations of high redshift Type Ia supernovae which suggest an accelerating universe. A flat accelerating universe is strongly favoured by combining supernovae observations with observations of CMB anisotropies on degree scales which give the ‘best-fit’ values Θ_A ⋍ 0.7 and Θ _m ⋍ 0.3. A time dependent cosmological A-term can be generated by scalar field models with exponential and power law potentials. Some of these models can alleviate the ‘fine tuning’ problem which faces the cosmological constant.     

Random Matrix Theory and L-Functions at s= 1/2

Recent results of Katz and Sarnak [8, 9] suggest that the low-lying zeros of families of L-functions display the statistics of the eigenvalues of one of the compact groups of matrices U(N), O(N) or USp(2N). We here explore the link between the value distributions of the L-functions within these families at the central point s= 1/2 and those of the characteristic polynomials Z(U,θ) of matrices U with respect to averages over SO(2N) and USp(2N) at the corresponding point θ= 0, using techniques previously developed for U(N) in [10]. For any matrix size N we find exact expressions for the moments of Z(U,0) for each ensemble, and hence calculate the asymptotic (large N) value distributions for Z(U,0) and log Z(U,0). The asymptotic results for the integer moments agree precisely with the few corresponding values known for L-functions. The value distributions suggest consequences for the non-vanishing of L-functions at the central point. Received: 1 February 2000 / Accepted: 24 March 2000     

Is the Pioneer Anomaly a Counter Example to the Dark Matter Hypothesis?

The Hubble law is extended to massive particles based on the de Broglie wavelength. Due to the expansion of the universe the wavelength of an unbound particle would increase according to its cosmological redshift. Based on the navigation anomalies of the Pioneer 10 & 11 spacecraft it is postulated that an unbound massive particle has a cosmological redshift z=(c/v ₀)H ₀ t, where c is the speed of light in vacuum, v ₀ is the initial velocity of the particle, H ₀ is Hubble’s constant and t is the duration of time that the particle has been unbound. The increase in wavelength of the particle corresponds to a decrease in its speed by Δv=−cH ₀ t. Furthermore, it is hypothesized that the solar system has escaped the gravity of the Galaxy as evidenced by its orbital speed and radial distance and by the visible mass within the solar system radius. This means that spacecraft which become unbound to the solar system would also be galactically unbound and subject to the Hubble law. This hypothesis and the extended Hubble law may explain the anomalous acceleration found to be acting upon the unbound Pioneer 10 & 11 spacecraft. Thus, the Pioneer anomaly may be a counter example to the dark matter hypothesis. Because photons have a speed which make them unbound to the Galaxy, it is predicted that the navigation beam in open space would undergo a cosmological redshift in its frequency which would be detectable with modern clocks.     

Fitting Cosmological Data to the Function <Emphasis Type="Italic">q</Emphasis>(<Emphasis Type="Italic">z</Emphasis>) from GR Theory: Modified Chaplygin Gas

In the Friedmann cosmology, the deceleration of the expansion q plays a fundamental role. We derive the deceleration as a function of redshift q(z) in two scenarios: ΛCDM model and modified Chaplygin gas (MCG) model. The function for the MCG model is then fitted to the cosmological data in order to obtain the cosmological parameters that minimize χ ². We use the Fisher matrix to construct the covariance matrix of our parameters and reconstruct the q(z) function. We use Supernovae Ia, WMAP5, and BAO measurements to obtain the observational constraints. We determined the present acceleration as q ₀ = − 0.65 ±0.19 for the MCG model using the Union2 dataset of SNeIa, BAO, and CMB and q ₀ = − 0.67 ±0.17 for the Constitution dataset, BAO and CMB. The transition redshift from deceleration to acceleration was found to be around 0.80 for both datasets. We have also determined the dark energy parameter for the MCG model: Ω _X0 = 0.81 ±0.03 for the Union2 dataset and Ω _X0 = 0.83 ±0.03 using the Constitution dataset.     

Cosmological models and latest observational data

In this note, we consider the observational constraints on some cosmological models by using the 307 Union type Ia supernovae (SNIa), the 32 calibrated gamma-ray bursts (GRBs) at z>1.4, the updated shift parameter R from WMAP 5-year data (WMAP5), and the distance parameter A of the measurement of the baryon acoustic oscillation (BAO) peak in the distribution of SDSS luminous red galaxies with the updated scalar spectral index n _s from WMAP5. The tighter constraints obtained here update the ones obtained previously in the literature.     

第Ⅱ类两态叠加多模叠加态光场的非线性高阶压缩特性研究

本文根据量子力学中的线性叠加原理,构造了由多模(即q模)虚相干态|{iZ_j}>_q及其相反态|{-iZ_j}>_q的线性叠加所组成的第Ⅱ类两态叠加多模叠加态光场|ψ₂⁽²⁾>_q.利用新近建立的有关双模及多模辐射场的非线性高阶压缩理论,首次对态|ψ₂⁽²⁾>_q的两种非线性高阶压缩(即N次方Y压缩和N次方H压缩)效应进行了详细研究。结果表明:1)当N为奇数时,如果各模的初始相位满足一定的量子化条件,而态间的初始相位差在其态间压缩区内连续变化;或者态间的初始相位差取某一特定值,而各模的初始相位在其腔模压缩区内连续变化时,态|ψ₂⁽²⁾>_q就会呈现出周期性变化的、任意阶的N次方Y压缩效应。2)当q·N为奇数时,如果各模的初始相位和满足一定的量子化条件,而态间的初始相位差在上述的态间压缩区内连续变化;或者态间的初始相位差取上述的某一固定值,而各模的初始相位和在其腔模和压缩区内连续变化时,态|ψ₂⁽²⁾>_q就呈现出周期性变化的、任意阶的N次方H压缩效应。3)与文献10相比,态|ψ₂⁽²⁾>_q与态|ψ(2)1>_q这两者之间的压缩情况正好相反。