1,829 research outputs found
Stark Effect Revisited
We extend the rigorous theory of complex scaling to atoms in constant electric field. This allows one to give a precise mathematical definition of resonance and leads to several results about the perturbation series: Borel summability at nonreal field and a relation between the asymptotics of the perturbation coefficients for large n and the width of the resonance for small field
A Variational Approach to the Spinless Relativistic Coulomb Problem
By application of a straightforward variational procedure we derive a simple,
analytic upper bound on the ground-state energy eigenvalue of a
semirelativistic Hamiltonian for (one or two) spinless particles which
experience some Coulomb-type interaction.Comment: 7 pages, HEPHY-PUB 606/9
Relativistic Coulomb Problem: Analytic Upper Bounds on Energy Levels
The spinless relativistic Coulomb problem is the bound-state problem for the
spinless Salpeter equation (a standard approximation to the Bethe--Salpeter
formalism as well as the most simple generalization of the nonrelativistic
Schr\"odinger formalism towards incorporation of relativistic effects) with the
Coulomb interaction potential (the static limit of the exchange of some
massless bosons, as present in unbroken gauge theories). The nonlocal nature of
the Hamiltonian encountered here, however, renders extremely difficult to
obtain rigorous analytic statements on the corresponding solutions. In view of
this rather unsatisfactory state of affairs, we derive (sets of) analytic upper
bounds on the involved energy eigenvalues.Comment: 12 pages, LaTe
The matrix factorisations of the D-model
The fundamental matrix factorisations of the D-model superpotential are found
and identified with the boundary states of the corresponding conformal field
theory. The analysis is performed for both GSO-projections. We also comment on
the relation of this analysis to the theory of surface singularities and their
orbifold description.Comment: 23 pages, LaTe
Integrability of the N=2 boundary sine-Gordon model
We construct a boundary Lagrangian for the N=2 supersymmetric sine-Gordon
model which preserves (B-type) supersymmetry and integrability to all orders in
the bulk coupling constant g. The supersymmetry constraint is expressed in
terms of matrix factorisations.Comment: LaTeX, 19 pages, no figures; v2: title changed, minor improvements,
refs added, to appear in J. Phys. A: Math. Ge
Moduli Webs and Superpotentials for Five-Branes
We investigate the one-parameter Calabi-Yau models and identify families of
D5-branes which are associated to lines embedded in these manifolds. The moduli
spaces are given by sets of Riemann curves, which form a web whose intersection
points are described by permutation branes. We arrive at a geometric
interpretation for bulk-boundary correlators as holomorphic differentials on
the moduli space and use this to compute effective open-closed superpotentials
to all orders in the open string couplings. The fixed points of D5-brane moduli
under bulk deformations are determined.Comment: 41 pages, 1 figur
D-brane superpotentials and RG flows on the quintic
The behaviour of D2-branes on the quintic under complex structure
deformations is analysed by combining Landau-Ginzburg techniques with methods
from conformal field theory. It is shown that the boundary renormalisation
group flow induced by the bulk deformations is realised as a gradient flow of
the effective space time superpotential which is calculated explicitly to all
orders in the boundary coupling constant.Comment: 24 pages, 1 figure, v2:Typo in (3.14) correcte
Stark Effect Revisited
We extend the rigorous theory of complex scaling to atoms in constant electric field. This allows one to give a precise mathematical definition of resonance and leads to several results about the perturbation series: Borel summability at nonreal field and a relation between the asymptotics of the perturbation coefficients for large n and the width of the resonance for small field
Calculations for Mirror Symmetry with D-branes
We study normal functions capturing D-brane superpotentials on several one-
and two-parameter Calabi-Yau hypersurfaces and complete intersections in
weighted projective space. We calculate in the B-model and interpret the
results using mirror symmetry in the large volume regime, albeit without
identifying the precise A-model geometry in all cases. We identify new classes
of extensions of Picard-Fuchs equations, as well as a novel type of topology
changing phase transition involving quantum D-branes. A 4-d domain wall which
is obtained in one region of closed string moduli space from wrapping a
four-chain interpolating between two Lagrangian submanifolds is, for other
values of the parameters, represented by a disk ending on a single Lagrangian.Comment: 42 page
Reaction Networks For Interstellar Chemical Modelling: Improvements and Challenges
We survey the current situation regarding chemical modelling of the synthesis
of molecules in the interstellar medium. The present state of knowledge
concerning the rate coefficients and their uncertainties for the major
gas-phase processes -- ion-neutral reactions, neutral-neutral reactions,
radiative association, and dissociative recombination -- is reviewed. Emphasis
is placed on those reactions that have been identified, by sensitivity
analyses, as 'crucial' in determining the predicted abundances of the species
observed in the interstellar medium. These sensitivity analyses have been
carried out for gas-phase models of three representative, molecule-rich,
astronomical sources: the cold dense molecular clouds TMC-1 and L134N, and the
expanding circumstellar envelope IRC +10216. Our review has led to the proposal
of new values and uncertainties for the rate coefficients of many of the key
reactions. The impact of these new data on the predicted abundances in TMC-1
and L134N is reported. Interstellar dust particles also influence the observed
abundances of molecules in the interstellar medium. Their role is included in
gas-grain, as distinct from gas-phase only, models. We review the methods for
incorporating both accretion onto, and reactions on, the surfaces of grains in
such models, as well as describing some recent experimental efforts to simulate
and examine relevant processes in the laboratory. These efforts include
experiments on the surface-catalysed recombination of hydrogen atoms, on
chemical processing on and in the ices that are known to exist on the surface
of interstellar grains, and on desorption processes, which may enable species
formed on grains to return to the gas-phase.Comment: Accepted for publication in Space Science Review
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