A Realization of Yangian and Its Applications in Addition of Angular Momenta

A realization of Yangian associated with SL(2) has been constructed. Using its shift operators, we discuss Clebsch-Gordan coefficients and other applications in addition of angular momenta.     

Gravitomagnetic Measurement of the Angular Momentum of Celestial Bodies

The asymmetry in the time delay for light rays propagating on opposite sides of a spinning body is analyzed. A frequency shift in the perceived signals is found. A practical procedure is proposed for evidencing the asymmetry, allowing for a measurement of the specific angular momentum of the rotating mass. Orders of magnitude are considered and discussed.     

Dark Energy and Global Rotation of the Universe

We discuss the problem of universe acceleration driven by global rotation. The redshift-magnitude relation is calculated and discussed in the context of SN Ia observation data. It is shown that the dynamics of considered problem is equivalent to the Friedmann model with additional non-interacting fluid with negative pressure. We demonstrate that the universe acceleration increase is due to the presence of global rotation effects, although the cosmological constant is still required to explain the SN Ia data. We discuss some observational constraints coming from SN Ia imposed on the behaviour of the homogeneous Newtonian universe in which matter rotates relative local gyroscopes. In the Newtonian theory _r,0 can be identified with ^,0 (only dust fluid is admissible) and rotation can exist with _r,0 =^,0 0. However, the best-fit flat model is the model without rotation, i.e., ^,0 =0. In the considered case we obtain the limit for ^,0>-0.033 on the confidence level 68.3. We are also beyond the model and postulate the existence of additional matter which scales like radiation matter and then analyse how that model fits the SN Ia data. In this case the limits on rotation coming from BBN and CMB anisotropies are also obtained. If we assume that the current estimates are _m,0 ~ 0.3, _r,0 ~ 10^-4, then the SN Ia data show that ^,0 -0.01 (or ₀ > 2.6 · 10^-19 rad/s). The statistical analysis gives us that the interval for any matter scaling like radiation is _r,0 ( - 0.01, 0.04).     

Letter: Density Perturbations in a Universe Dominated by the Chaplygin Gas

We study the fate of density perturbations in a Universe dominate by the Chaplygin gas, which exhibit negative pressure. In opposition to other models of perfect fluid with negative pressure, there is no instability in the small wavelength limit, due to the fact that the sound velocity for the Chaplygin gas is positive. We show that it is possible to obtain the value for the density contrast observed in large scale structure of the Universe by fixing a free parameter in the equation of state of this gas. The negative character of pressure must be significant only very recently.     

Letter: Irreversible Processes in a Universe Modelled as a Mixture of a Chaplygin Gas and Radiation

The evolution of a Universe modelled as a mixture of a Chaplygin gas and radiation is determined by taking into account irreversible processes. This mixture could interpolate periods of a radiation dominated, a matter dominated and a cosmological constant dominated Universe. The results of a Universe modelled by this mixture are compared with the results of a mixture whose constituents are radiation and quintessence. Among other results it is shown that: (a) for both models there exists a period of a past deceleration with a present acceleration; (b) the slope of the acceleration of the Universe modelled as a mixture of a Chaplygin gas with radiation is more pronounced than that modelled as a mixture of quintessence and radiation; (c) the energy density of the Chaplygin gas tends to a constant value at earlier times than the energy density of quintessence does; (d) the energy density of radiation for both mixtures coincide and decay more rapidly than the energy densities of the Chaplygin gas and of quintessence.     

Open Cosmologies with Rotation

We study a rotating and expanding, Gödel type metric, originally considered by Korotkii and Obukhov [1, 2], showing that, in the limit of large times and nearby distances, it reduces to the open metric of Friedmann. In the epochs when radiation or dust matter dominate the energy density, our solutions are similar to the isotropic ones and, in what concerns processes occurring at small times, the rotation leads only to higher order corrections. At large times, the solution is dominated by a decaying positive cosmological term, with negative pressure, and necessarily describes a quasi-flat universe if the energy conditions have to be satisfied. The absence of closed time-like curves requires a superior limit for the global angular velocity, which appears as a natural explanation for the observed smallness of the present rotation. The conclusion is that the introduction of a global rotation, in addition to be compatible with observation, can enrich the standard model of the Universe, explaining issues like the origin of galaxies rotation and the quasi-flatness problem.     

碳酸钙微粒光致旋转的实验和理论研究

理论分析了由于光束轨道角动量和自旋角动量传递以及微粒的特殊形状导致微粒旋转的机理.实验建立了单光束激光光镊装置,不仅可以捕获并移动直径为微米量级的微小粒子,而且利用圆偏振光与微粒之间角动量的传递,实现了对具有双折射特性的碳酸钙微粒的光致旋转.实验中发现微粒的旋转不仅取决于光束的偏振态,还与微粒本身的形状有关,解释了实验中观察到的几种旋转现象.碳酸钙微粒旋转的最高转速达到12转/秒,转速与激光功率成正比.     

在空间转动变换下的角动量本征态随转角的参变数演变的路径积分

研究在空间转动变换下，直接采用转轴的方向角与转角描述角动量本征态的演变过程，并建立一般角动量转动矩阵元以及多重转动矩阵元随转角θ的参变数λ（０→θ）演变的路径积分；给出处理泛函（路径）积分为普通多重积分的一般方法。     

Entropy of the Universe and Standard Cosmology

By means of a variant approach to Standard Relativistic Cosmology, we hint that the entropy of the Universe is growing with t ^3/2, where t stands for time-coordinate. Then, the absolute temperature obeys Standard t ^−1/2-dependence. We make contact with our previous paper (Berman, Int. J. Theor. Phys., 2009), in the context of a Machian Universe; but we also consider the dependencies of the scale-factor and energy density, with time, as in Standard treatments.     

Robertson-Walker Fluid Sources Endowed with Rotation Characterised by Quadratic Terms in Angular Velocity Parameter

Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented up to and including quadratic terms in angular velocity parameter. A family of analytic solutions are obtained for the case in which the source angular velocity is purely time-dependent. A subclass of solutions is presented which merge smoothly to homogeneous rotating and non-rotating central sources. The particular solution for dust endowed with rotation is presented. In all cases explicit expressions, depending sinusoidally on polar angle, are given for the density and internal supporting pressure of the rotating source. In addition to the non-zero axial velocity of the fluid particles it is shown that there is also a radial component of velocity which vanishes only at the poles. The velocity four-vector has a zero component between poles.     

The first second of the Universe

The history of the Universe after its first second is now tested by high quality observations of light element abundances and temperature anisotropies of the cosmic microwave background. The epoch of the first second itself has not been tested directly yet; however, it is constrained by experiments at particle and heavy ion accelerators. Here I attempt to describe the epoch between the electroweak transition and the primordial nucleosynthesis. The most dramatic event in that era is the quark‐hadron transition at 10 μs. Quarks and gluons condense to form a gas of nucleons and light mesons, the latter decay subsequently. At the end of the first second, neutrinos and neutrons decouple from the radiation fluid. The quark‐hadron transition and dissipative processes during the first second prepare the initial conditions for the synthesis of the first nuclei. As for the cold dark matter (CDM), WIMPs (weakly interacting massive particles) – the most popular candidates for the CDM – decouple from the presently known forms of matter, chemically (freeze‐out) at 10 ns and kinetically at 1 ms. The chemical decoupling fixes their present abundances and dissipative processes during and after thermal decoupling set the scale for the very first WIMP clouds.     

Entropy of the Universe

After a discussion on several limiting cases where General Relativity turns into less sophisticated theories, we find that in the correct thermodynamical and cosmological weak field limit of Einstein’s field equations the entropy of the Universe is R ^3/2-dependent, where R stands for the radius of the causally related Universe. Thus, entropy grows in the Universe, contrary to Standard Cosmology prediction.     

Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

Modern Cosmological Data and Rotation of the Universe

A new nonstationary rotating cosmological model is developed which describes the evolution of the observed Universe, since its properties are in good agreement with recent astronomical observations. It is demonstrated that the energy density of cosmological rotation can play a role of dark energy and induce the accelerated expansion of the Universe detected recently. In some situations when the causality parameter of the rotating cosmological model is negative, the cosmological rotational energy can be represented as phantom matter that violates the weak energy condition p + ε ≥ 0. The suggested cosmological model has no initial singularity, that is, the cosmological rotation can prevent the formation of the singularity.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 3–6, March, 2005.     

Connection Between Angular Momenta of the Hydrogen Atom and a Four-Dimensional Harmonic Oscillator

After remadeling the form of the Kustaanheimo-Stiefel transformation, all the problems on the connection between angular momenta of the hydrogen atom and a four-dimensional harmonic oscillator are studied.     

Calculation of the Energy of Excited States with Zero Electron Orbital Angular Momenta

Russian Physics Journal - Within the framework of the variational method, as the result of a numerical calculation we have found the energy of the excited state and the screening constant of the...     

Acceleration Field of a Universe Modeled as a Mixture of Scalar and Matter Fields

A model of the Universe as a mixture of a scalar (inflaton or rolling tachyon from the string theory) and a matter field (classical particles) is analyzed. The particles are created at the expense of the gravitational energy through an irreversible process whereas the scalar field is supposed to interact only with itself and to be minimally coupled with the gravitational field. The irreversible processes of particle creation are related to the non-equilibrium pressure within the framework of the extended (causal or second-order) thermodynamic theory. The scalar field (inflaton or tachyon) is described by an exponential potential density added by a parameter which represents its asymptotic value and can be interpreted as the vacuum energy. This model can simulate three phases of the acceleration field of the Universe, namely, (a) an inflationary epoch with a positive acceleration followed by a decrease of the acceleration field towards zero, (b) a past decelerated period where the acceleration field decreases to a maximum negative value followed by an increase towards zero, and (c) a present accelerated epoch. For the energy densities there exist also three distinct epochs which begin with a scalar field dominated period followed by a matter field dominated epoch and coming back to a scalar field dominated phase.     

Basic Aspect of Relativistic Rotation: Franklin Rotation of a Sphere

We give a relativistic treatment to the dynamics of spherical bodies rotating at very high speed. It is found that most of the mass of a homogeneous spherical quark with Franklin rotation is due to the relativistic increase of the mass.     

Letter: Thermodynamical Properties of Metric Fluctuations During Inflation

I study a thermodynamical approach to scalar metric perturbations during the inflationary stage. In the power-law expanding universe here studied, I find a negative heat capacity as a manifestation of superexponential growing for the number of states in super Hubble scales. The power spectrum depends on the Gibbons-Hawking and Hagedorn temperatures.