14 research outputs found
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
(with , 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 . 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