Bound states of the Klein-Gordon equation for vector and scalar general Hulthen-type potentials in D-dimension

We solve the Klein-Gordon equation in any $D$-dimension for the scalar and vector general Hulth\'{e}n-type potentials with any $l$ by using an approximation scheme for the centrifugal potential. Nikiforov-Uvarov method is used in the calculations. We obtain the bound state energy eigenvalues and the corresponding eigenfunctions of spin-zero particles in terms of Jacobi polynomials. The eigenfunctions are physical and the energy eigenvalues are in good agreement with those results obtained by other methods for D=1 and 3 dimensions. Our results are valid for $q=1$ value when $l\neq 0$ and for any $q$ value when $l=0$ and D=1 or 3. The $s$% -wave ($l=0$) binding energies for a particle of rest mass $m_{0}=1$ are calculated for the three lower-lying states $(n=0,1,2)$ using pure vector and pure scalar potentials.Comment: 25 page

Polarizing primordial gravitational waves by parity violation

We study primordial gravitational waves (PGWs) in the Horava-Lifshitz (HL) theory of quantum gravity, in which high-order spatial derivative operators, including the ones violating parity, generically appear in order for the theory to be power-counting renormalizable and ultraviolet (UV) complete. Because of both parity violation and non-adiabatic evolution of the modes due to a modified dispersion relationship, a large polarization of PGWs becomes possible, and it could be well within the range of detection of the BB, TB and EB power spectra of the forthcoming cosmic microwave background (CMB) observations.Comment: revtex4, 3 figures. Phys. Rev. D87, 103512 (2013

Bound State Solutions of Klein-Gordon Equation with the Kratzer Potential

The relativistic problem of spinless particle subject to a Kratzer potential is analyzed. Bound state solutions for the s-wave are found by separating the Klein-Gordon equation in two parts, unlike the similar works in the literature, which provides one to see explicitly the relativistic contributions, if any, to the solution in the non-relativistic limit.Comment: 6 page

General covariant Horava-Lifshitz gravity without projectability condition and its applications to cosmology

We consider an extended theory of Horava-Lifshitz gravity with the detailed balance condition softly breaking, but without the projectability condition. With the former, the number of independent coupling constants is significantly reduced. With the latter and by extending the original foliation-preserving diffeomorphism symmetry ${{Diff}}(M, {\cal{F}})$ to include a local U(1) symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related to them disappear, including the instability, strong coupling, and different speeds in the gravitational sector. When the theory couples to a scalar field, we find that the scalar field is not only stable in both the ultraviolet (UV) and infrared (IR), but also free of the strong coupling problem, because of the presence of high-order spatial derivative terms of the scalar field. Furthermore, applying the theory to cosmology, we find that due to the additional U(1) symmetry, the Friedmann-Robertson-Walker (FRW) universe is necessarily flat. We also investigate the scalar, vector, and tensor perturbations of the flat FRW universe, and derive the general linearized field equations for each kind of the perturbations.Comment: 19 pages, comments are welcome!!

A Modified Synchrotron Model for Knots in the M87 Jet

For explaining the broadband spectral shape of knots in the M87 jet from radio through optical to X-ray, we propose a modified synchrotron model that considers the integrated effect of particle injection from different acceleration sources in the thin acceleration region. This results in two break frequencies at two sides of which the spectral index of knots in the M87 jet changes. We discuss the possible implications of these results for the physical properties in the M87 jet. The observed flux of the knots in the M87 jet from radio to X-ray can be satisfactorily explained by the model, and the predicted spectra from ultraviolet to X-ray could be further tested by future observations. The model implies that the knots D, E, F, A, B, and C1 are unlikely to be the candidate for the TeV emission recently detected in M87.Comment: 12 pages, 1 figure, 2 tables, Accepted for publication in ApJ Letter

Alternative scheme to generate a supersinglet state of three-level atoms

In this paper we propose an alternative scheme to generate a supersinglet state of three three-level atoms via a single-mode of a cavity QED based on the two-photon transitions described by the 'full microscopical Hamiltonian approach'. In it, three three-level atoms prepared in suitable initial states are sequentially sent through the cavity originally prepared in its vacuum state. After an appropriate choice of the atom-cavity interaction times plus a field detection the state that describes the whole atom-field system is projected in the desired supersinglet state. The fidelity and success probability of the state as well as the practical feasibility of the scheme are discussed.Comment: 10 pages, 3 figures, 4 table

Interior estimates of derivatives and a Liouville type theorem for Parabolic kk-Hessian equations

In this paper, we establish the gradient and Pogorelov estimates for $k$-convex-monotone solutions to parabolic $k$-Hessian equations of the form $-u_t\sigma_k(\lambda(D^2u))=\psi(x,t,u)$. We also apply such estimates to obtain a Liouville type result, which states that any $k$-convex-monotone and $C^{4,2}$ solution $u$ to $-u_t\sigma_k(\lambda(D^2u))=1$ in $\mathbb{R}^n\times(-\infty,0]$ must be a linear function of $t$ plus a quadratic polynomial of $x$, under some growth assumptions on $u$.Comment: 14 page