Scalar kinks and fermion localisation in warped spacetimes

Scalar kinks propagating along the bulk in warped spacetimes provide a thick brane realisation of the braneworld. We consider here, a class of such exact solutions of the full Einstein-scalar system with a sine-Gordon potential and a negative cosmological constant. In the background of the kink and the corresponding warped geometry, we discuss the issue of localisation of spin half fermions (with emphasis on massive ones) on the brane in the presence of different types of kink-fermion Yukawa couplings. We analyse the possibility of quasi-bound states for large values of the Yukawa coupling parameter $\gamma_F$ (with $\nu$, the warp factor parameter kept fixed) using appropriate, recently developed, approximation methods. In particular, the spectrum of the low--lying states and their lifetimes are obtained, with the latter being exponentially enhanced for large $\nu \gamma_F$. Our results indicate quantitatively, within this model, that it is possible to tune the nature of warping and the strength and form of the Yukawa interaction to obtain trapped massive fermion states on the brane, which, however, do have a finite (but very small) probability of escaping into the bulk.Comment: 22 pages, 4 figures, RevTex

Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pade resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317, p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pade approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results enhanced; one section and one appendix added and some minor changes and additions; to appear in phys. rev.

Low-energy unphysical saddle in polynomial molecular potentials

Vibrational spectra of polyatomic molecules are often obtained from a polynomial expansion of the adiabatic potential around a minimum. For several molecules, we show that such an approximation displays an unphysical saddle point of comparatively small energy, leading to a region where the potential is negative and unbounded. This poses an upper limit for a reliable evaluation of vibrational levels. We argue that the presence of such saddle points is general.Comment: The preprint version of the published Mol. Phys. paper, 19 pages, 3 figure

Multidimensional WKB Approximation for Tunneling Along Curved Escape Paths

Asymptotics of the perturbation series for the ground state energy of the coupled anharmonic oscillators for the positive coupling constant is related to the lifetime of the quasistationary states for the negative coupling constant. The latter is determined by means of the multidimensional WKB approximation for tunneling along curved escape paths. General method for obtaining such approximation is described. The cartesian coordinates (x,y) are choosen in such a way that the x-axis has the direction of the probability flux at large distances from the well. The WKB wave function is then obtained by the simultaneous expansion of the wave function in the coordinate y and the parameter γ determining the curvature of the escape path. It is argued, both physically and mathematically, that these two expansions are mutually consistent. Several simplifications in the integrations of equations are pointed out. It is shown that to calculate outgoing probability flux it is not necessary to deal with inadequacy of the WKB approximation at the classical turning point. The WKB formulas for the large-order behavior of the perturbation series are compared with numerical results and an excellent agreement between the two is found. KEY WORDS: multidimensional wkb approximation; large-order behavior of the perturbation series. 1