Mass hierarchy, mass gap and corrections to Newton’s law on thick branes with Poincaré symmetry

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schrödinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with $m^2\ge 0$ , in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza–Klein (KK) excitations and to analytically compute the corrections to Newton’s law in the thin brane limit. In the first case we consider a novel solution with a mass gap in the spectrum of KK fluctuations with two bound states—the massless 4D graviton free of tachyonic instabilities and a massive KK excitation—as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the thin Randall–Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved with positive branes as in the Lykken–Randall (LR) model and the model is completely free of naked singularities. We also show that the scalar–tensor system is stable under scalar perturbations with no scalar modes localized on the braneworld configuration.     

Setting initial conditions for inflation with reaction–diffusion equation

We discuss the issue of setting appropriate initial conditions for inflation. Specifically, we consider natural inflation model and discuss the fine tuning required for setting almost homogeneous initial conditions over a region of order several times the Hubble size which is orders of magnitude larger than any relevant correlation length for field fluctuations. We then propose to use the special propagating front solutions of reaction–diffusion equations for localized field domains of smaller sizes. Due to very small velocities of these propagating fronts we find that the inflaton field in such a field domain changes very slowly, contrary to naive expectation of rapid roll down to the true vacuum. Continued expansion leads to the energy density in the Hubble region being dominated by the vacuum energy, thereby beginning the inflationary phase. Our results show that inflation can occur even with a single localized field domain of size smaller than the Hubble size. We discuss possible extensions of our results for different inflationary models, as well as various limitations of our analysis (e.g. neglecting self gravity of the localized field domain).     

Effective Mass Dirac--Morse Problem with any κ-value

The Dirac-Morse problem is investigated within the framework of an approximation to the term proportional to 1/r^2 in the view of the position-dependent mass formalism. The energy eigenvalues and corresponding wave functions are obtained by using the parametric generalization of the Nikiforov-Uvarov method for any R-value. We also study the approximate energy eigenvalues, and the corresponding wave functions in the case of the constant-mass for pseudospin, and spin cases, respectively.     

Dibaryon Mass and Width Calculation with Tensor Interaction

The effect of tensor interaction due to gluon and Goldstone boson exchange on the dibaryon mass and decay width has been studied in the framework of the quark delocalization and colour screening model. The effective S-D wave transition interactions induced by gluon and Goldstone boson exchanges decrease quickly with the increasing channel strangeness, and there is no six-quark state in the light flavour world, which can become a bound one by the help of these tensor interactions, except for the deuteron. The K and η meson exchange effect has been shown to be negligible after a short-range truncation in this model approach. The partial D-wave decay widths, from the NΩ state to the AΞ final states of spins 0 and 1, are 20.7 keV and 63.1 keV respectively. This is a very narrow dibaryon resonance, that might be detected in the relativistic heavy ion reaction by the existing RHIC detectors through the reconstruction of the AΞ vertex mass and by the future COMPAS detector at CERNand the FAIR project in Germany.     

Semiclassical Method to Schroedinger Equation with Position-Dependent Effective Mass

In this paper, two novel semiclassical methods including the standard and supersymmetric WKB quantization conditions are suggested to discuss the Schroedinger equation with position-dependent effective mass. From a proper coordinate transformation, the formalism of the Schroedinger equation with position-dependent effective mass is mapped into isospectral one with constant mass and therefore for a given mass distribution and physical potential function the bound state energy spectrum can be determined easily by above method associated with a simple integral formula. It is shown that our method can give the analytical results for some exactly-solvable quantum systems.     

Improved Quark Mass Density-Dependent Model with Non-Linear Scalar Interaction

We present an improved quark mass density-dependent model which includes the quark and non-linear scalar field coupling. The wavefunction of quark is given. The rms charge radius, the magnetic moment, and the ratio between the axial-vector and the vector β-decay coupling constants of the nucleon are calculated. We find that the results given the present model are in agreement with experiments.     

Deformation of LeBrun’s ALE Metrics with Negative Mass

In this article we investigate deformations of a scalar-flat Kähler metric on the total space of complex line bundles over ${\mathbb{CP}^1}$ constructed by C. LeBrun. In particular, we find that the metric is included in a one-dimensional family of such metrics on the four-manifold, where the complex structure in the deformation is not the standard one.     

The Vlasov–Poisson System with Infinite Mass and Energy

This paper deals with solutions to the Vlasov–Poisson system with an infinite mass. The solution to the Poisson equation cannot be defined directly because the macroscopic density is constant at infinity. To solve this problem, we decompose the solution to the kinetic equation into a homogeneous function and a perturbation. We are then able to prove an existence result in short time for weak solutions to the equation for the perturbation, even though there are no a priori estimates by lack of positivity.     

Anti-holomorphic involutive isometry of hyper-Kähler manifolds and branes

We study complex Lagrangian submanifolds of a compact hyper-Kähler manifold and prove two results: (a) that an involution of a hyper-Kähler manifold which is antiholomorphic with respect to one complex structure and which acts non-trivially on the corresponding symplectic form always has a fixed point locus which is complex Lagrangian with respect to one of the other complex structures, and (b) there exist Lagrangian submanifolds which are complex with respect to one complex structure and are not the fixed point locus of any involution which is anti-holomorphic with respect to one of the other complex structures.     

How probable is inflation?

The Henneaux-Gibbons-Hawking-Stewart canonical measure on the set of classical universes is applied to a Friedmann-Robertson-Walker model containing a massive scalar field. Although a uniform probability distribution in this measure would solve the flatness problem, it gives an ambiguous probability for inflation, since both the set of inflationary solutions and the set of noninflationary solutions have infinite measure.     

Polarons with Spatially Dependent Mass in a Finite Parabolic Quantum Well

We study the energy levels of an electron (or hole) polaron in a parabolic quantum well structure,including the spatial dependence of the effective mass.We also consider the two-mode behaviour of longitudinal optical phonon modes of the ternary mixed crystals in the structure,in the calculation of the effect of the electron phonon interaction.We calculate the ground state,the first excited state and the transition energy of an electron (or hole) in the GaAs/AlxGa1-xAs parabolic quantum well structure.The numerical results show that the electron-phonon interaction obviously affects the energy levels of the electron (or hole),which are in agreement with experimental results.     

Cosmological Kaluza–Klein branes in black brane spacetimes

We discuss the cosmological evolution of a brane in the D(>6)$D(>6)$-dimensional black brane spacetime in the context of the Kaluza–Klein (KK) braneworld scheme, i.e., to consider KK compactification on the brane. The bulk spacetime is composed of two copies of a patch of D  -dimensional black three-brane solution. The near-horizon geometry is given by AdS₅×S(D−5)${\mathit{AdS}}_5\times S^{(D-5)}$ while in the asymptotic infinity the spacetime approaches D-dimensional Minkowski. We consider the brane motion from the near-horizon region toward the spatial infinity, which induces cosmology on the brane. As is expected, in the early times, namely when the brane is located in the near-horizon region, the effective cosmology on the brane coincides with that in the second Randall–Sundrum (RS II) model. Then, the brane cosmology starts to deviate from the RS type one since the dynamics of KK compactified dimensions becomes significant. We find that the brane Universe cannot reach the asymptotic infinity, irrespectively of the components of matter on the brane.     

Variations of the Speed of Light with Frequency and Implied Photon Mass

A general frequency-dependent dispersion relation of the speed of light in different mediums （vacuum, insulator, plasma） is deduced based on the Proca equations. Several recent astronomical observations of the pulsars are used to set the limits on the photon rest mass by this method and several upper bounds of larger than one order improvement than previous similar results are obtained. Considering the dispersion of the massive photon, the possible upper limits on the photon rest mass are also derived from the recently experimental results for testing the constancy of the speed of light in special relativity.     

On the Mass Concentration for Bose–Einstein Condensates with Attractive Interactions

We consider two-dimensional Bose–Einstein condensates with attractive interaction, described by the Gross–Pitaevskii functional. Minimizers of this functional exist only if the interaction strength a satisfies ${a < a^* = \|Q\|_2^2}$ , where Q is the unique positive radial solution of ${\Delta u - u + u^3 = 0}$ in ${\mathbb{R}^2}$ . We present a detailed analysis of the behavior of minimizers as a approaches a*, where all the mass concentrates at a global minimum of the trapping potential.     

Remarks on Exact Solvability of Quantum Systems with Spatially Varying Effective Mass

Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable onedimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported in the literature and clarifies the relation between physically acceptable effective mass Hamiltonians.