On the possibility of measuring the gravitational interaction of the neutron with a macroscopic body

The possibility of experimentally observing the gravitational interaction of the neutron with a macroscopic body is discussed. It is shown that the sensitivity of neutron-optics experiments may be one to two orders of magnitude higher than that which is necessary for observing the gravitational effect. Either the deflection of the neutron trajectory in the gravitational field of a heavy attractor or the gravitation-induced shift of the neutron-wave phase can be recorded experimentally.     

The gravitational contribution to the stress-energy tensor of a medium in general relativity

The macroscopic stress-energy tensor of an astronomical medium such as a galaxy of stars is determined by the field equation of general relativity from the small-scale variations in mass and velocity. In the weak-field, slow-motion approximation, in which the gravitational fields of the stars are Newtonian, it is found that the contribution by the small-scale gravitational fields to the macroscopic density and stress are, respectively, the Newtonian gravitational energy density and the Newtonian gravitational stress tensor. This result is based on the general-relativity field equation, not conservation laws, although the general-relativity field equation has the well-known property of being consistent with conservation laws.     

Microscopic gravity as a yang-mills field

The equation of a microscopic gravitational field as a Yang-Mills field is postulated. We consider the mechanism of introducing matter field masses and a classical macroscopic gravitational field, which is described by the Einstein equation (generally, with Λ-term).     

Multi-species two-level atomic media displaying electromagnetic left handedness

A multi-species two-level atomic system, the simplest being a representative two species collection of atoms studied here, contained in either a gaseous host medium or as dopants in a solid state host medium, determines the macroscopic permittivity and permeability seen by a probe field. Electronic or optical state initialization prepares the diagonal density matrix. Multi-species design of the atomic system allows assignment of different constituent densities in relation to the electric or magnetic matrix elements, generating left-handed electrodynamics in some detuning regions of the probe field.     

Multipole structure of static continuous matter distributions in general relativity

A mass skeleton is defined for a static extended body in a gravitational field. It is a scalar-valued distribution on a tangent space, and is equivalent to that part of the reduced multipole moment structure which describes the mass density of the body. An explicit form is given for this distribution in terms of the mass density and the scalar potential of the field. It is deduced that the mass skeleton and the scalar potential are not completely independent. The smoothness of the mass distribution imposes certain weak restrictions on those scalar potentials which are compatible with a given mass skeleton.Dedicated to Achille Papapetrou on the occasion of his retirement.     

不同电场下碳纳米管场致发射电流密度研究

本文运用密度泛函理论和金属电子论, 深入研究了碳纳米管场致发射电流的变化规律. 结果显示其发射电流密度取决于体系的态密度、赝能隙、管长和局域电场, 在不同范围电场下的变化规律不同. 在较低电场下, 发射电流密度随电场增强而近似线性增大(对应的宏观电场须小于18 V· μm^-1); 但在较高电场下, 发射电流密度随外电场增加呈现非周期性振荡增长趋势, 碳纳米管表现为电离发射. 本文进一步研究了金属性碳纳米管电导率在不同电场下的变化规律.     

Is gravitational mass of a composite quantum body equivalent to its energy?

We define passive gravitational mass operator of a hydrogen atom in the post-Newtonian approximation of general relativity and show that it does not commute with energy operator, taken in the absence of gravitational field. Nevertheless, the equivalence between the expectation values of passive gravitational mass and energy is shown to survive for stationary quantum states. Inequivalence between passive gravitational mass and energy at a macroscopic level results in time dependent oscillations of the expectation values of passive gravitational mass for superpositions of stationary quantum states, where the equivalence restores after averaging over time. Inequivalence between gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by the atoms, supported and moved in the Earth gravitational field with constant velocity using spacecraft or satellite, which can be experimentally measured.     

Radiation from a Charge Supported in a Gravitational Field

We examine whether a charge supported statically in a gravitational field radiates, and find the answer to this question to be positive. Based on our earlier results we find that the important condition for the creation of radiation is the existence of a relative acceleration between the charge and its electric field, where such an acceleration causes the curving of the electric field and the creation of a stress force due to this curvature. This stress force is the reaction force, which creates the radiation. Later we find that this condition do exist for a charge supported statically in a gravitational field, where the electric field of the charge falls in the gravitational field, it curves, and the stress force raised in this curved field, creates electromagnetic radiation.     

Classes of exact Einstein–Maxwell solutions

We find new classes of exact solutions to the Einstein–Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein–Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.     

Electric charge of a lightning ball

The electric charge of a lightning ball is found by comparing the electrohydrodynamic stabilities of a charged drop in an electrostatic suspension and a lightning ball floating in a superposition of the gravitational field and the surface electric field. It has been assumed that the electric field strength at the surface is limited by a breakdown value. For a lightning ball radius of 15 cm, its charge is estimated as several microcoulombs. Accordingly, the density of electrostatic energy accumulated in the lightning ball is on the order of one-hundredth of a joule per square centimeter. The density of the material that constitutes the lightning ball has been estimated for the case when the electric field strength at the site of its origination is several times higher than that in fine weather. The density of the lightning ball turns out to differ from that of air by only a few percents.     

Cosmological solutions in macroscopic gravity

In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the equations of macroscopic gravity for a spatially homogeneous and isotropic macroscopic space-time and find that the correlation tensor is of the form of a spatial curvature term. We briefly discuss the physical consequences of these results.     

One-dimensional Rydberg gas in a magnetoelectric trap

We study the quantum properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap which is superimposed by a homogeneous electric field. Trapped Rydberg atoms can be created in long-lived electronic states exhibiting a permanent electric dipole moment of several hundred Debye. The resulting dipole-dipole interaction in conjunction with the radial confinement is demonstrated to give rise to an effectively one-dimensional ultracold Rydberg gas with a macroscopic interparticle distance. We derive analytical expressions for the electric dipole moment and the required linear density of Rydberg atoms.     

Rydberg states of hydrogenlike ions in a braneworld model

Precise measurements of optical transition frequencies between Rydberg states of hydrogen-like ions could be used to obtain an improved value of the Rydberg constant, by avoiding the uncertainties about the proton radius. Motivated by this perspective, we investigate the influence of the gravitational interaction on the energy levels of Hydrogen-like ions in Rydberg states in a braneworld model. As it is known, in this scenario, the gravitational interaction is amplified in short distances. We show that, for Rydberg states, the main contribution for the gravitational potential energy does not come from the rest energy concentrated on the nucleus but from the energy of the electromagnetic field created by its electric charge. The reason is connected to the fact that, when the ion is in a Rydberg state with high angular momentum, the gravitational potential is not computable in zero-width brane approximation due to the gravitational influence of the electrovacuum in which the lepton is moving. Considering a thick brane scenario, we calculate the gravitational potential energy associated to the nucleus charge in terms of the confinement parameter of the electric field in the brane. We show that the gravitational effects on the energy levels of a Rydberg state can be amplified by hidden dimensions even when the compactification scale is shorter than the Bohr radius.     

Reciprocity in electrohydrodynamics

We consider a rigid body of arbitrary shape with a permanent charge distribution and a permanent dielectric profile immersed in a fluid with a frequency dependent dielectric constant. The body performs small oscillatory translational and rotational motions and the whole system is subjected to an applied electric field oscillating at the same frequency. The force and torque on the body and its external dipole moment are related by a resistance matrix to the translational and rotational velocity and the applied electric field. We show on the basis of the equations of linear electrohydrodynamics that the resistance matrix is symmetric. This may be regarded as an example of Onsager symmetry.     

Concerning Measurement of Gravitomagnetism in Electromagnetic Systems

Measurement of gravitomagnetic field is of fundamental importance as a test of general relativity. Here we present a new theoretical project for performing such a measurement based on detection of the electric field arising from the interplay between the gravitomagnetic and magnetic fields in the stationary axial-symmetric gravitational field of a slowly rotating massive body. Finally it is shown that precise magnetometers based on superconducting quantum interferometers could not be designed for measurement of the gravitomagnetically induced magnetic field in the cavity of a charged capacitor since they measure the circulation of a vector potential of electromagnetic field, i.e., an invariant quantity including the sum of electric and magnetic fields, and the general-relativistic magnetic part will be totally cancelled by the electric one which is in good agreement with the experimental results.     

On particle creation by black holes

Hawking's analysis of particle creation by black holes is extended by explicitly obtaining the expression for the quantum mechanical state vector ψ which results from particle creation starting from the vacuum during gravitational collapse. (Hawking calculated only the expected number of particles in each mode for this state.) We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. In agreement with previously known results, we find that we are led to a unique quantum scattering theory which is completely well behaved mathematically provided a certain condition is satisfied by the operators which describe the scattering of classical positive frequency solutions. In terms of these operators we derive the expression for the state vector describing particle creation from the vacuum, and we prove that S-matrix is unitary. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. There is some ambiguity in the theory in this case arising from freedom involved in defining what one means by “positive frequency” at the future event horizon. However, it is proven that the expression for the density matrix formed from ψ describing the emission of particles to infinity is independent of this choice, and thus unambiguous predictions for the results of all possible measurements at infinity are obtained. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail (i.e., not only in expected number of particles) with black body emission.     

Temperature and current density distributions at spark plasma sintering of inhomogeneous samples

We analyze the effect of inhomogeneity in the properties of a material on the conditions of obtaining thermoelectrics by spark plasma sintering. Inclusions localized and distributed over the volume of materials with different values of electric and thermal conductivities are considered. It is found that the presence of macroscopic inhomogeneities changes the current density distribution in the cross section of the sample being sintered. It is shown that inhomogeneity in the properties of materials during sintering do not substantially affect the temperature field in the sample at the macroscopic level, but change the current density distribution profile. The ranges of variation of the current density in the regions with inhomogeneous electric and thermal conductivities are determined for various types of macroscopically inhomogeneous inclusions and their distribution. The applicability of various models for describing spark plasma sintering is considered.     

Bose-Einstein condensates beyond mean field theory: quantum backreaction as decoherence

We propose an experiment to measure the slow log(N) convergence to mean field theory (MFT) around a dynamical instability. Using a density matrix formalism instead of the standard macroscopic wave function approach, we derive equations of motion which go beyond MFT and provide accurate predictions for the quantum break time. The leading quantum corrections appear as decoherence of the reduced single-particle quantum state.     

Poisson-Vlasov: stochastic representation and numerical codes

In this paper, we examine the effects of the gravitational field on the dynamical evolution of the cavity-field entropy and the creation of the Schr?dinger-cat state in the Jaynes-Cummings model. We consider a moving two-level atom interacting with a single mode quantized cavity-field in the presence of a classical homogeneous gravitational field. Based on an su(2) algebra, as the dynamical symmetry group of the model, we derive the reduced density operator of the cavity-field which includes the effects of the atomic motion and the gravitational field. Also, we obtain the exact solution and the approximate solution for the system-state vector, and examine the atomic dynamics. By considering the temporal evolution of the cavity-field entropy as well as the dynamics of the Q-function of the cavity-field we study the effects of the gravitational field on the generation of the Schr?dinger-cat states of the cavity-field by using the Q-function, field entropy and approximate solution for the system-state vector. The results show that the gravitational field destroys the generation of the Schr?dinger-cat state of the cavity-field.