Number Conservation Law Research Articles

Cosmological particle creation in conformal gravity

We constructed conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from usual hydrodynamical de- scription of particle motion written in Eulerian coordinates we substituted particle number conservation law (which enters formalism) by the particle creation law, proportional to square of Weyl tensor (following famous result by Ya. B. Zel'dovich and A. A. Starobinsky). Then, demanding conformal invariance of whole dynamical system, we have got both (Weyl)-conformal gravity and Einstein-Hilbert-dilaton gravity action integral. Thus, we obtained something like induced gravity suggested first by A. D. Sakharov. It is shown that resulting system is self-consistent. Some future developments of theory are discussed in concluding Chapter.

Statistical mechanics of two-dimensional foams: Physical foundations of the model.

In a recent series of papers, a statistical model that accounts for correlations between topological and geometrical properties of a two-dimensional shuffled foam has been proposed and compared with experimental and numerical data. Here, the various assumptions on which the model is based are exposed and justified: the equiprobability hypothesis of the foam configurations is argued. The range of correlations between bubbles is discussed, and the mean-field approximation that is used in the model is detailed. The two self-consistency equations associated with this mean-field description can be interpreted as the conservation laws of number of sides and bubble curvature, respectively. Finally, the use of a "Grand-Canonical" description, in which the foam constitutes a reservoir of sides and curvature, is justified.

A unified model with a generalized gauge symmetry and its cosmological implications

A unified model is based on a generalized gauge symmetry with groups [SU3c]color×(SU2×U1)× [U1b×U1l]. It implies that all interactions should preserve conservation laws of baryon number, lepton number, and electric charge, etc. The baryonic U1b, leptonic U1l and color SU3c gauge transformations are generalized to involve nonintegrable phase factors. One has gauge invariant fourth-order equations for massless gauge fields, which leads to linear potentials in the [U1b×U1l] and color [SU3c] sectors. We discuss possible cosmological implications of the new baryonic gauge field. It can produce a very small constant repulsive force between two baryon galaxies (or between two anti-baryon galaxies), where the baryon force can overcome the gravitational force at very large distances and leads to an accelerated cosmic expansion. Based on conservation laws in the unified model, we discuss a simple rotating dumbbell universe with equal amounts of matter and anti-matter, which may be pictured as two gigantic rotating clusters of galaxies. Within the gigantic baryonic cluster, a galaxy will have an approximately linearly accelerated expansion due to the effective force of constant density of all baryonic matter. The same expansion happens in the gigantic anti-baryonic cluster. Physical implications of the generalized gauge symmetry on charmonium confining potentials due to new SU3c field equations, frequency shift of distant supernovae Ia and their experimental tests are discussed.

Numerical models of cosmological evolution of a degenerate Fermi-system of scalar charged particles

Based on the previously constructed mathematical model of a statistical Fermi system with particle interaction, in this paper we construct and analyze numerical models of cosmological evolution of a single-component degenerate Fermi system of scalar particles. The applied mathematics package Mathematica 9 is used for numerical model construction. It is strictly proved that the conservation law for the total energy of the scalarly charged degenerate Fermi system and a massive scalar field is a differential consequence of the particle number conservation law. Thus the mathematical model of cosmological evolution of the system is reduced to a closed normal set of three essentially nonlinear ordinary differential equations. After transforming the equations to dimensionless variables, an algorithm of its numerical solution is suggested. On the basis of numerical simulation of the cosmological evolution we show the presence of a new phenomenon in the cosmological evolution: it is the phenomenon of phantom bursts of cosmological acceleration at times of the order of 103 Planck times.

Multi-symplectic scheme for the coupled Schrödinger—Boussinesq equations

In this paper, a multi-symplectic Hamiltonian formulation is presented for the coupled Schrödinger—Boussinesq equations (CSBE). Then, a multi-symplectic scheme of the CSBE is derived. The discrete conservation laws of the Langmuir plasmon number and total perturbed number density are also proved. Numerical experiments show that the multi-symplectic scheme simulates the solitary waves for a long time, and preserves the conservation laws well.

Majorana mass, time reversal symmetry, and the dimension of space

The Weyl fermions with a well defined chirality are known to demand that the dimension of space which they inhabit must be odd. It is shown here, however, that not all odd dimensional spaces are equally good hosts: in particular, an arbitrary number of chiral Weyl fermions can acquire a Majorana mass only in three (modulo eight) dimensions. The argument utilizes a) the precise analogy that exists between the Majorana mass term and the Cooper pairing of time-reversed Weyl fermions, and b) the conditions on the requisite time-reversal operator, which are implied by the Clifford algebra. The theorem connects the observed odd number of neutrino flavors, the time reversal symmetry, and the dimension of our space, and strengthens the argument for the possible violation of the lepton number conservation law.

Lattice Boltzmann method for relativistic hydrodynamics: Issues on conservation law of particle number and discontinuities

In this paper, we aim to address several important issues about the recently developed lattice Boltzmann (LB) model for relativistic hydrodynamics [M. Mendoza et al., Phys. Rev. Lett. 105, 014502 (2010); Phys. Rev. D 82, 105008 (2010)]. First, we study the conservation law of particle number in the relativistic LB model. Through the Chapman-Enskog analysis, it is shown that in the relativistic LB model the conservation equation of particle number is a convection-diffusion equation rather than a continuity equation, which makes the evolution of particle number dependent on the relaxation time. Furthermore, we investigate the origin of the discontinuities appeared in the relativistic problems with high viscosities, which were reported in a recent study [D. Hupp et al., Phys. Rev. D 84, 125015 (2011)]. A multiple-relaxation-time (MRT) relativistic LB model is presented to examine the influences of different relaxation times on the discontinuities. Numerical experiments show the discontinuities can be eliminated by setting the relaxation time $\tau_e$ (related to the bulk viscosity) to be sufficiently smaller than the relaxation time $\tau_v$ (related to the shear viscosity). Meanwhile, it is found that the relaxation time $\tau_\varepsilon$, which has no effect on the conservation equations at the Navier-Stokes level, will affect the numerical accuracy of the relativistic LB model. Moreover, the accuracy of the relativistic LB model for simulating moderately relativistic problems is also investigated.

On the integrating cavity transfer function and decay time

A novel method for deriving the integrating cavity transfer function, where the average electromagnetic radiation intensity decay time in the cavity has been found as the final result, is presented, and where a uniform photon distribution inside the cavity was assumed. Instead of the beam reflection analysis, the method is based on employing the energy conservation law inside the integrating cavity. The obtained result for the decay time is slightly different from other results obtained elsewhere but still in relatively good agreement with them. In order to verify the obtained result, we performed a similar analysis based on the photon number conservation law. This analysis gives the same result for the decay time as the first one. Finally, in order to confirm the obtained result, we statistically analyzed the average lifetime of a photon inside the cavity after the radiation source switch-off, i.e. the average time between the radiation source switch-off and its absorption by the cavity inner walls. The result for the decay time obtained in this way is identical to the results obtained using the above-presented methods. At the end, the transfer function of the integrating cavity filled with a weak absorbing material is derived. Based on the obtained result, a novel method for the absorption coefficient measurement is proposed.

Establishing the Presence of Coherence in Atomic Fermi Superfluids: Spin-Flip and Spin-Preserving Bragg Scattering at Finite Temperatures

We show how in ultracold Fermi gases the difference between the finite temperature T structure factors, called S_(ω,q), associated with spin and density, reflects coherent order at all ω, q, k(F)a, and T. This observation can be exploited in two photon Bragg scattering experiments on gases which are subject to variable attractive interactions. Our calculations incorporate spin and particle number conservation laws which lead to compatibility at general T with two f-sum rules. Because of its generality a measurement of S_(ω,q) can be a qualitative, direct, in situ approach for establishing superfluid order.

Double beta decays and neutrino nuclear responses

Neutrino-less double beta decays ( 0 ν β β ), which violate the lepton number conservation law by Δ L = 2 , are unique and realistic probes for studying the Majorana nature of neutrinos, the ν mass spectrum and the absolute mass scale, the lepton sector CP and others beyond the standard electro-weak theory. Neutrino nuclear responses (nuclear matrix elements M 0 ν ) are crucial to extract neutrino properties of the particle physics interests from experimental 0 ν β β rates. Subjects discussed include 0 ν β β processes and Majorana neutrinos, the present and future 0 ν β β experiments, and neutrino nuclear responses ( M 0 ν ) and charge exchange reactions.

YANG–MILLS GRAVITY IN FLAT SPACE–TIME II: GRAVITATIONAL RADIATIONS AND LEE–YANG FORCE FOR ACCELERATED COSMIC EXPANSION

Within Yang–Mills gravity with translation group T(4) in flat space–time, the invariant action involving quadratic translation gauge-curvature leads to quadrupole radiations, which are shown to be consistent with experiments. The radiation power turns out to be the same as that in Einstein's gravity to the second-order approximation. We also discuss an interesting physical reason for the accelerated cosmic expansion based on the long-range Lee–Yang force of Ub(1) gauge field associated with the established conservation law of baryon number. We show that the Lee–Yang force can be related to a linear potential ∝ r, provided the gauge field satisfies a fourth-order differential equation in flat space–time. Furthermore, we consider an experimental test of the Lee–Yang force related to the accelerated cosmic expansion. The necessity of generalizing Lorentz transformations for accelerated frames of reference and accelerated Wu–Doppler effects are briefly discussed.

Structure analysis of multiphase systems by anomalous small-angle X-ray scattering

The theory of small-angle scattering is reviewed with special attention paid to the anomalous scattering and multiphase systems. A general equation is derived that describes the scattering of a multiphase system as a sum of scattering functions of each of the phases, as if it scattered alone in a two-phase system, and interphase interference scattering functions. These scattering functions depend only on the spatial distribution of the phase boundaries, but not on the scattering density. Contrast variation techniques are most rewarding when the scattering density of only one phase can be varied. For anomalous small-angle X-ray scattering (ASAXS), this means the most favourable is the case in which resonant atoms are contained in one phase only. The general equation involves n(p − 1) unknown partial atomic number density differences, where p is the number of phases and n the number of the different atom types in the sample. These partial atomic number density differences can be found if a suitable structure model is applied to calculate the phase scattering functions. Then, the phase compositions and densities can be calculated by solving a system of linear equations incorporating the atom number conservation law. The partial structure factors formalism is also reviewed. Corresponding equations for a system of n types of atoms and p phases are derived. The number of independent partial structure factors is p(p − 1)/2 and depends on the number of phases, but not on the number of the types of the atoms in the sample, as in the case of wide-angle scattering.

Description of spin transport and precession in spin-orbit coupling systems and general equation of continuity

By generalizing the usual current density to a matrix with respect to spin variables, a general equation of continuity satisfied by the density matrix and current density matrix has been derived. This equation holds in arbitrary spin-orbit coupling systems as long as its Hamiltonian can be expressed in terms of a power series in momentum. Thereby, the expressions of the current density matrix and a torque density matrix are obtained. The current density matrix completely describes both the usual current and spin current as well; while the torque density matrix describes the spin precession caused by a total effective magnetic field, which may include a realistic and an effective one due to the spin-orbit coupling. In contrast to the conventional definition of spin current, this expression contains an additional term if the Hamiltonian includes nonlinear spin-orbit couplings. Moreover, if the degree of the full Hamiltonian $\geq3$, then the particle current must also be modified in order to satisfy the local conservation law of number.

Double Beta Decays and Neutrino Masses

Neutrino-less double beta decays (0νββ), which violate the lepton number conservation law by Δ L = 2, are of great interest for studying the fundamental properties of neutrinos beyond the standard ...

Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation

We have calculated the self-consistent Green's function for a number of atoms and diatomic molecules. This Green's function is obtained from a conserving self-energy approximation, which implies that the observables calculated from the Green's functions agree with the macroscopic conservation laws for particle number, momentum, and energy. As a further consequence, the kinetic and potential energies agree with the virial theorem, and the many possible methods for calculating the total energy all give the same result. In these calculations we use the finite temperature formalism and calculate the Green's function on the imaginary time axis. This allows for a simple extension to nonequilibrium systems. We have compared the energies from self-consistent Green's functions to those of nonselfconsistent schemes and also calculated ionization potentials from the Green's functions by using the extended Koopmans' theorem.

Relaxation of an electron system: Conserving approximation

The dynamic response of an interacting electron system is determined by an extension of the relaxation-time approximation forced to obey local conservation laws for number, momentum and energy. A consequence of these imposed constraints is that the local electron equilibrium distribution must have a space- and time-dependent chemical potential, drift velocity and temperature. Both quantum kinetic and semi-classical arguments are given, and we calculate and analyze the corresponding analytical d-dimensional dielectric function. Dynamical correlation, arising from relaxation effects, is shown to soften the plasmon dispersion of both two- and three-dimensional systems. Finally, we consider the consequences for a hydrodynamic theory of a d-dimensional interacting electron gas, and by incorporating the competition between relaxation and inertial effects we derive generalised hydrodynamic equations applicable to arbitrary frequencies.

Inversion method approach to the quantum kinetic equation: inhomogeneous case

The inversion method to derive the quantum kinetic equation is extended to the case of an inhomogeneous system. Within the closed-time-path formalism, the source is introduced to probe the (Fourier transform of the) Wigner distribution function and the equation of motion for the Wigner function is derived perturbatively by the inversion formulae. The equation of motion has the form of the generalized Boltzmann equation, which is non-local in space and time. For the obtained kinetic equation, the local conservation laws of number, energy and momentum are confirmed.

Analyses of collective flow and space-time evolution based on relativistic hydrodynamical model

We numerically solve fully (3+1)-dimensional relativistic hydrodynamical equation with the baryon number conservation law. For realistic initial conditions we adopt the results from the event generator (URASiMA). Using this model we discuss collective flow.

Well-posedness of the Hydrodynamic Model for Semiconductors

This paper concerns the well-posedness of the hydrodynamic model for semiconductor devices, a quasilinear elliptic-parbolic-hyperbolic system. Boundary conditions for elliptic and parabolic equations are Dirichlet conditions while boundary conditions for the hyperbolic equations are assumed to be well-posed in L2 sense. Maximally strictly dissipative boundary conditions for the hyperbolic equations satisfy the assumption of well-posedness in L2 sense. The well-posedness of the model under the boundary conditions is demonstrated. This paper addresses the well-posedness of the hydrodynamic model for semiconductors. The model is derived from moments of the Boltzmann’s equation, taken over group velocity space. When coupled with the charge conservation equation, it describes the behaviour of small semiconductor devices and accounts for special features such as hot electrons and velocity overshoots. The model consists of a set of non-linear conservation laws for particle number, momentum, and energy, coupled to Poisson’s equation for the electric potential. It is a perturbation of the drift diffusion model [7]. We consider a ballistic diode problem which models the channel of a MOSFET, so the effect of holes in the model can be neglected. The model is [4,11]

Vector Implementation of Nonlinear Monte Carlo Coulomb Collisions

A nonlinear Monte Carlo collision model based on Coulomb binary collisions is presented with emphasis on its efficient implementation. The presented Monte Carlo collision operator, which has a simple form, fulfills particle number, momentum, and energy conservation laws quasi-locally and is equivalent to the nonlinear Fokker–Planck operator in the limit of infinitesimally small time interval of the binary collisions. Two vectorizable algorithms are designed for its fast implementation. Drastic speedup is obtained by the algorithms on vector computers. Various test simulations regarding relaxation processes, electrical conductivity, etc. are carried out in the velocity space. The test results, which are in good agreement with theories, and timing results on vector computers show that the present collision model is practically applicable.