The calculation of Dirac sea effects on finite solitons

The effects of polarization of the Dirac sea on finite solitons in a simple theory in which fermions interact with a single scalar field are studied. The mass shift for a given background scalar field is computed numerically and compared to approximations arising from expansions in inverse powers of the effective fermion mass and in powers of derivatives of the background scalar field. The conditions under which such approximations succeed are discussed. When such approximations work one can derive local equations of motion for the soliton fields which include the effects of polarizing the Dirac sea. These new equations are studied and energy minimization is used to explore the effects of the Dirac sea on the structure of the soliton. Calculations for a typical Friedberg-Lee soliton are presented, and it is shown that, while the approximations do not work well for fields employed to model the quark structure of nucleons, they do provide an upper bound for the mass of the soliton. A scalar field typical of those used to model ¹⁶O in quantum hadrodynamics is also studied, and it is shown that, when the effective potential is supplemented by the next term occurring in a derivative expansion, the renormalized shift in the energy of the Dirac sea is well approximated.     

K-essential covariant holography

Braneworld models may yield interesting effects ranging from high-energy physics to cosmology, or even some low-energy physics. Their mode structure modifies standard results in these physical realms that can be tested and used, for example, to set bounds on the models parameters. Now, to define braneworld deviations from standard 4D physics, a notion of matter and gravity localization on the brane is crucial. In this work we investigate the localization of universal massive scalar fields in a de Sitter thick tachyonic braneworld generated by gravity coupled to a tachyonic bulk scalar field. This braneworld possesses a 4D de Sitter induced metric and is asymptotically flat despite the presence of a negative bulk cosmological constant, a novel and interesting peculiarity that contrasts with previously known models. It turns out that universal scalar fields can be localized in this expanding braneworld if their bulk mass obeys an upper bound, otherwise the scalar fields delocalize: The dynamics of the scalar field is governed by a Schrödinger equation with an analog quantum mechanical potential of modified Pöschl–Teller type. This potential depends on the bulk curvature of the braneworld system as well as on the value of the bulk scalar field mass. For masses satisfying a certain upper bound, the potential displays a negative minimum and possesses a single massless bound state separated from the Kaluza–Klein (KK) massive modes by a mass gap defined by the Hubble (expansion scale) parameter of the 3-brane. As the bulk scalar field mass increases, the minimum of the quantum mechanical potential approaches a null value and, when the bulk mass reaches certain upper bound, it becomes positive (eventually transforming into a potential barrier), leading to delocalization of the bulk scalar field from the brane. We present analytical expressions for the general solution of the Schrödinger equation. Thus, the KK massive modes are given in terms of general Heun functions as well as the expression for the massless zero mode, giving rise to a new application of these special functions.     

Structure of elementary particles in a nonlinear field theory

Characteristics of nonlinear gauge-invariant singularity-free field theories of elementary particles are discussed. It is shown that the electromagnetic field, in conjunction with a scalar field which is required for gauge invariance, provides a potential mechanism for the creation of the spin and magnetic moment of the particle, in addition to its mass and charge.     

Full phase diagram of the massive Gross-Neveu model

The massive Gross-Neveu model is solved in the large-N limit at finite temperature and chemical potential. The scalar potential is given in terms of Jacobi elliptic functions. It contains three parameters which are determined by transcendental equations. Self-consistency of the scalar potential is proved. The phase diagram for non-zero bare quark mass is found to contain a kink-antikink crystal phase as well as a massive fermion gas phase featuring a cross-over from light to heavy effective fermion mass. For zero bare quark mass, we recover the three known phases kink-antikink crystal, massless fermion gas, and massive fermion gas. All phase transitions are shown to be of second order. Equations for the phase boundaries are given and solved numerically. Implications on condensed matter physics are indicated where our results generalize the bipolaron lattice in non-degenerate conducting polymers to finite temperature.     

Metric for an Oblate Earth

In linearized general relativity the metric ofa body is described by a scalar potential and athree-vector potential. We here present a simpletransformation derivation of the linearized metric interms of these potentials, and calculate the exactscalar and vector potentials for a field with oblatespheroidal symmetry. The results for the externalpotentials do not depend on details of the densitydistribution inside the earth; both the scalar and vectorpotentials are fully determined by the total mass, thetotal angular momentum, and a radial parameter, all ofwhich are accurately known from observation. The scalar potential is accurate to roughly10^-6 and the vector potential, which hasnever been accurately measured, should be accurate toabout 10^-5. Applications include an accuratetreatmen t of the details of the motion of satellites, and theprecession of a gyroscope in earth orbit.     

Effective Masses of Pentaquark Θ+ in Nuclear Matter

The properties of baryons in nuclear matter are analysed in the relativistic mean-field theory(RMF). It is found that the scalar field σ meson affects the properties of baryon at high density. A density dependent scalar coupling gσN is determined according to the idea of quark-meson coupling model and extended to RMF. It is shown that gσN affects the property of nuclear matter weakly at low density, but strongly at high density. The relation between the scalar density ρ_S and the nuclear density ρ and the effective mass of the pentaquark Θ⁺ are studied with the density dependent coupling constant. The density dependent scalar coupling obviously affects the effective masses of baryons in nuclear matter, especially at high density.     

Conformally coupled scalar field solutions and the cosmological constant

Solutions are presented for a scalar field coupled conformally to Einstein gravity with a nonvanishing cosmological constant, in the case that the spacetime metric is spatially homogeneous and isotropic. Since the cosmological constant destroys the conformal invariance of the action, these solutions cannot be obtained by solving the flat space wave equation for the scalar field. It turns out that the metric is determined entirely by the cosmological constant, while the scalar field acquires an apparent mass squared which is proportional to the cosmological constant. It is conjectured that the cosmological constant in the universe at present may thus be disguised as the mass of some scalar field.     

Casimir Effect of Massive Scalar Field with Hybrid Boundary Condition in （1＋1）-Dimensional Spacetime

The Casimir energy of massive scalar field with hybrid （Diriehlet-Neumann） boundary condition is calculated. In order to regularize the model, the typical methods named as mode summation method and Green＇s function method are used respectively. It is found that the regularized zero-point energy density depends on the scalar field＇s mass. When the field is massless, the result is consistent with previous literatures.     

Modified gravity inspired DGP brane cosmology

We consider a DGP brane scenario where a scalar field is present on the brane through the introduction of a scalar potential, itself motivated by the notion of modified gravity. This theory predicts that the mass appearing in the gravitational potential is modified by the addition of the mass of the scalar field. The cosmological implications that such a scenario entails are examined and shown to be consistent with a universe expanding with power-law acceleration.     

Nucleons in nuclei in the selfconsistent soliton model to QCD

In the scalar Soliton model of QCD the gluon field operators are replaced by a classical selfcoupling scalar field with solitontype interaction. The quark wave-functions and the soliton field are calculated for the free nucleon as compared to a nucleon inside nuclear matter approximated by averaged boundary conditions to simulate the surrounding nucleons. The mass of the nucleon as well as its mean effective radius are given in terms of the nuclear-matter density and the model parameters. For large quark-soliton coupling the EMC-effect is seen, and then at high densities a plasma of free quarks and free localized solitons is the lowest energy solution.     

Scalar flux in a uniform mean scalar gradient in homogeneous isotropic steady turbulence

Statistics of a passive scalar flux in a uniform mean scalar gradient convected by homogeneous isotropic steady turbulence are numerically studied by using very high resolution direct numerical simulation. It is found that the Nusselt number increases in proportion to the Péclet number and that the one point probability density function of the scalar flux is negatively skewed and exponential, and is insensitive to the variation of the Péclet number. The scalar field is studied by visualization, and the ramp-cliff structure and the mesa-canyon structure are observed along the directions parallel and perpendicular to the mean scalar gradient, respectively. The probability density function of the scalar flux is theoretically computed and found to be in good agreement with the numerical results. A Lagrangian statistical theory for the scalar flux is developed, which predicts that the scalar transfer flux is given by the time integral of the Lagrangian velocity autocorrelation and increases in proportion to the Péclet number, which is consistent with the results of the direct numerical simulation. A physical explanation of the asymmetry of the scalar flux PDF is explored.     

Limits on inflationary models of the universe

It is shown that there are severe limits on any model in which the universe undergoes a period of exponential expansion in the early stages. If one requires that the exponential expansion is long enough to account for the spatial flatness of the universe and that it should not create larger density fluctuations than are observed, it follows that the Hubble constant during the exponential expansion cannot be greater than 6 × 10^?5 of the Planck mass. This rules out all models in which the Hubble constant is of the order of the Planck mass. It is shown that one can satisfy the limits with a model containing a massive scalar field if the mass of the field is less than about 10¹⁴ GeV.     

Field-dependent coupling strength for scalar fields

Effective Lagrangians with a nonlinear coupling between the scalar density of the nucleons and the scalar meson field are investigated within the framework of relativistic mean-field theories. This phenomenological coupling acts as a field-dependent coupling strength and is supposed to take into account renormalization effects within a mean-field picture. The parameters of the model are adjusted to saturation properties of nuclear matter and predictions for the real part of the optical potential are compared with experimental data. For that relativistic and nonrelativistic optical model fits are examined and an experimental standard is deduced which covers the energy range from ? 50 MeV to 1000 MeV. A definition for the real part of the optical potential is given which is not linear in the energy but has the proper limits for momentum zero and infinity. It is shown that for a special choice of the field-dependent coupling strength the meanfield theory can describe the nuclear equation of state and the momentum dependence of the single particle energy without further parameters up to momenta where the intrinsic structure of nucleon becomes relevant.     

Single field baryogenesis

We propose a new variant of the Affleck-Dine baryogenesis mechanism in which a rolling scalar field couples directly to left- and right-handed neutrinos, generating a Dirac mass term through neutrino Yukawa interactions. In this setup, there are no explicitly CP violating couplings in the Lagrangian. The rolling scalar field is also taken to be uncharged under the B - L quantum numbers. During the phase of rolling, scalar field decays generate a nonvanishing number density of left-handed neutrinos, which then induce a net baryon number density via electroweak sphaleron transitions.     

Irrotational Bianchi V viscous fluid cosmology with heat flux

The irrotational Bianchi V cosmological model under the influence of both shear and bulk viscosity, together with heat flux, has been studied. Exact solutions for the model are obtained with three assumptions of which the first two relate the matter density, shear scalar, and expansion scalar and the third is a barotropic equation of state, connecting the matter density and thermodynamic pressure. The properties of the solutions are studied and the temperature distribution is also given explicitly. It has been observed that along with the viscosity, heat flux further adds to the rate of entropy increase.     

Potential–density pairs for axisymmetric galaxies: the influence of scalar fields

We present a formulation for potential–density pairs to describe axi-symmetric galaxies in the Newtonian limit of scalar–tensor theories of gravity. The scalar field is described by a modified Helmholtz equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for axisymmetric systems and the multipole expansion of the Yukawa potential is given. In particular, we have computed potential–density pairs of galactic disks for an exponential profile and their rotation curves.     

On the calculation of matrix elements of one body operators in many nucleon systems

We demonstrate the connection between matrix elements of one body operators in odd nuclei and vertex functions. The procedure is free of assumptions on the pole distribution of the two point functions and it does not use perturbation theory. The renormalization of the external field, necessistated by configuration space limitations, is carried through for scalar, local fields, acting on the density and for radiation fields of the electric multipole type using the requirement of gauge invariance. It is shown that this renormalization is possible, even if the renormalized field is strongly energy dependent due to configuration mixing.     

Scalar particles mass spectrum and localization on FRW branes embedded in a 5D de Sitter bulk

In this paper, we study the scalar fields evolving on a FRW brane embedded in a five-dimensional de Sitter bulk. The scale function and the warp factor, solutions of the Einstein equations, are employed in the five-dimensional Gordon equation describing the massive scalar field, whose wave function depends on the cosmic time and on the extra-dimension. We point out the existence of bounded states and find a minimum value of the effective four-dimensional mass. For the test (scalar) field envelope along the extra-dimension, we derive the corresponding Schrödinger-like equation which is formally that for the Pöschl-Teller potential. Accordingly, we have obtained the quantization law for the mass parameter of the tested scalar field.     

Ab-initio calculations of electric field gradient in Ru compounds and their implication on the nuclear quadrupole moments of $$^{99}\hbox {Ru}$$ and $$^{101}\hbox {Ru}$$101Ru

We study a spatially homogeneous and anisotropic cosmological model in the Einstein gravitational theory with a minimally coupled scalar field. We consider a non-interacting combination of scalar field and perfect fluid as the source of matter components which are separately conserved. The dynamics of cosmic scalar fields with a zero rest mass and an exponential potential are studied, respectively. We find that both assumptions of potential along with the average scale factor as an exponential function of scalar field lead to the logarithmic form of scalar field in each case which further gives power-law form of the average scale factor. Using these forms of the average scale factor, exact solutions of the field equations are obtained to the metric functions which represent a power-law and a hybrid expansion, respectively. We find that the zero-rest-mass model expands with decelerated rate and behaves like a stiff matter. In the case of exponential potential function, the model decelerates, accelerates or shows the transition depending on the parameters. The isotropization is observed at late-time evolution of the Universe in the exponential potential model.     

温度与外磁场对Si均匀掺杂的GaAs量子阱电子态结构的影响

本文在有效质量近似下,通过自洽地求解薛定鄂方程及泊松方程计算了在温度T=273 K,磁感应强度B=25 T,Si均匀掺杂的GaAs/AlGaAs量子阱系统的电子态结构.研究了温度与外磁场对子带能量,本征包络函数,自洽势,电子密度分布,及费米能量的影响.发现在给定磁感应强度B=fi0下,随温度升高子带能量单调增加,费米能量单调递减,自洽势的势阱变深变陡,电子密度分布变宽,峰值降低;在给定温度下,随磁感应强度的增加子带能量及费米能量单调递增,自洽势阱变浅变宽,电子密度分布变窄,峰值升高.