Semiclassical corrections to the Einstein equation and Induced Matter Theory

The induced Einstein equation on a perturbed brane in the Induced Matter Theory is re-analyzed. We indicate that in a conformally flat background, the local quantum corrections to the Einstein equation can be obtained via the IMT. Using the FRW metric as the 4D gravitational model, we show that the classical fluctuations of the brane may be related to the quantum corrections to the classical Einstein equation. In other words, the induced Einstein equation on the perturbed brane can correspond with the semiclassical Einstein equation.     

Macroscopic Einstein equations to second order in the interaction constant

The present paper is a direct continuation of an earlier paper [JETP 83, 1 (1996)] devoted to the derivation of the macroscopic Einstein equations to within terms of second order in the interaction constant. Ensemble averaging of the microscopic Einstein equations and the Liouville equation for the random functions leads to a closed system of macroscopic Einstein equations and kinetic equations for one-particle distribution functions. The macroscopic Einstein equations differ from the classical equations in that their left-hand side contains additional terms due to particle interaction. The terms are traceless tensors with zero divergence. An explicit covariant expression for these terms is given in the form of momentum-space integrals of expressions dependent on one-particle distribution functions of the interacting particles of the medium. The given expressions are proportional to the cube of the Einstein constant and the square of the particle number density. The latter relationship implies that interaction effects manifest themselves in systems of very high density (the universe in the early stages of its evolution, dense objects close to gravitational collapse, etc.) Zh. éksp. Teor. Fiz. 112, 1153–1166 (October 1997)     

Higher order corrections in perturbative quantum chromodynamics

We present some techniques which have been developed recently or in the recent past to compute Feynman graphs beyond one-loop order. These techniques are useful to compute the three-loop splitting functions in QCD and to obtain the complete second order QED corrections to Bhabha scattering.     

Diffusive corrections to asymptotics of a strong-field quantum transport equation

The asymptotic analysis of a linear high-field Wigner-BGK equation is developed by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number ?, evolution equations are derived for the terms of zeroth and first order in ?. In particular, a quantum drift-diffusion equation for the position density of electrons, with an ?-order correction on the field terms, is obtained. Well-posedness and regularity of the approximate problems are established, and a rigorous proof that the difference between exact and asymptotic solutions is of order ?², uniformly in time and for arbitrary initial data is given.     

Next-to-leading order corrections to multiplicities

It is desirable to develop a systematic and practical method in perturbative QCD to analyze the semi-hard processes in the fragmentation of jets. In this paper, an integral equation with angular ordering is introduced to analyze the multiplicities of hadrons in high-energy jet productions. In order to demonstrate how the method works, the method is applied in the next-to-leading order to the energy dependence of the multiplicity and to the ratio of multiplicities in a gluon jet and in a quark jet. The results agree with the calculations done by Mueller by a different method.     

Planck-scale corrections to Friedmann equation

Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde’s proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde’s proposal and two known models of GUPs, we obtain modifications to Newton’s law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.     

From second to first order transitions in a disordered quantum magnet

The cross sections and transverse spin asymmetries in the hard exclusive electroproduction of decuplet baryons are calculated in the large N(c) limit and found to be comparable to that of octet baryons. Large N(c) selection rules for the production amplitudes are derived, leading to new sensitive tests of the spin aspects of the QCD chiral dynamics both in the nonstrange and strange sectors. Importance of such studies for the reliable extraction of the pion form factor from pion electroproduction is explained.     

Solution of the second order linear differential equation

An integro-iteration method is applied to solve the second order linear differential equation. Although the procedure is quite elementary it produces the general solution in form of a simple series which can be made to converge absolutely, at least in the region of interest. Particular solutions with given initial or boundary values can be readily obtained from the general solution.     

Higher order parabolic approximations of the reduced wave equation

Asymptotic solutions of order k⁻ⁿ are developed for the reduced wave equation. Here k is a dimensionless wave number and n is the arbitrary order of the approximation. These approximations are an extension of geometric acoustics theory and provide corrections to that theory in the form of multiplicative functions which satisfy parabolic partial differential equations. These corrections account for the diffraction effects caused by variation of the field normal to the ray path and the interaction of these transverse variations with the variation of the field along the ray. The theory is applied to the example of radiation from a piston, and it is demonstrated that the higher order approximations are more accurate for decreasing values of k.     

Wave function with second order correction and inflationary solutions in quantum cosmology

A brief account for the higher order wave function in Hartle-Hawking (H-H) proposal is given which is compared with the tunneling wave function due to Vilenkin. The probability distributions are determined for both types of wave functions. Also a class of solutions are evaluated using H-H approach for Kantowski-Sachs metric with a scalar field and inflation is observed.     

A proposal for detecting second order topological quantum phase

Gaussian linking of a semiclassical path of a charged particle with a magnetic flux tube is responsible for the Aharonov-Bohm effect, where one observes interference proportional to the magnitude of the enclosed flux. We construct quantum mechanical wave functions where semiclassical paths can have second order linking to two magnetic flux tubes, and show there is interference proportional to the product of the two fluxes.     

Einstein equation at singularities

Einstein’s equation is rewritten in an equivalent form, which remains valid at the singularities in some major cases. These cases include the Schwarzschild singularity, the Friedmann-Lemaître-Robertson-Walker Big Bang singularity, isotropic singularities, and a class of warped product singularities. This equation is constructed in terms of the Ricci part of the Riemann curvature (as the Kulkarni-Nomizu product between Einstein’s equation and the metric tensor).     

Higher order corrections to asymptotic-de Sitter inflation

Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter(d S) state during inflation. We use the asymptotic-d S mode to study the trans-Planckian correction of the power spectrum to the quasi-d S inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time(or gravitational waves) during inflation.As an important result, the amplitude of the power spectrum is dependent on the choice of c, i.e. the type of spacetime in the period of inflation. Also, the results are always valid for any asymptotic d S space-time and particularly coincide with the conventional results for d S and flat space-time.     

Higher order corrections and temperature effects to ion acoustic shock waves in quantum degenerate electron-ion plasma

The contribution of higher-order nonlinearity and dissipation to nonlinear ion acoustic shock waves (IASWs) is investigated by using the reductive perturbation technique in dense electron-ion plasma. The model consists of degenerate electrons (being either ultrarelativistic or nonrelativistic) and nonrelativistic ion fluid. A nonlinear Burger equation and a linear inhomogeneous Burger-type equation are derived. The inclusion of the higher-order corrections results in creating new shock wave structures, humped IASWs. It is found that the kinematic viscosity and the equilibrium ion number density play important roles in the basic features of the produced IA shocks and the associated electric fields. These findings are devoted to explaining the observed waves propagating in the outer periphery of compact dense stars which mostly consists of hydrogen and degenerate electrons.     

Higher order corrections to the Grimus-Stockinger formula

For the Grimus-Stockinger formula the same dimensionless parameter of asymptotic expansion is found by several ways of calculations. This parameter strongly depends on the width of wave packet.     

A second order numerical scheme for the improved Boussinesq equation

A finite-difference scheme arising from the use of rational approximants to the matrix-exponential term in a three-time level recurrence relation is used for the numerical solution of the improved Boussinesq equation (IBq). The resulting linear scheme, which is analyzed for local truncation error and stability, is tested numerically and conclusions with corresponding results known in the bibliography are derived.