Analytical solutions for a two-level system driven by a class of chirped pulses

We present analytical solutions for the problem of a two-level atom driven by a class of chirped pulses. The solutions are given in terms of Heun functions. Using appropriate chirping parameters an enhancement of four-orders of magnitudes in the population transfer is obtained.Comment: 5 pages, 5 figure

Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: l_{B} the magnetic length, l_{0} the Bohr radius and R the radius of the sphere. The energy spectrum of the particle is found by solving a Schr\"odinger equation of the Heun type, using the technique of continued fractions. It displays a rich set of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take definite values.Comment: 12 pages, 5 figures, accepted to JOPA, november 200

The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

We obtain isomonodromic transformations for Heun's equation by generalizing Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures finite-gap property. As an application, we prove conjectures in part III.Comment: 24 page

Geometric scaling in the spectrum of an electron captured by a stationary finite dipole

We examine the energy spectrum of a charged particle in the presence of a {\it non-rotating} finite electric dipole. For {\emph{any}} value of the dipole moment $p$ above a certain critical value p_{\mathrm{c}}$ an infinite series of bound states arises of which the energy eigenvalues obey an Efimov-like geometric scaling law with an accumulation point at zero energy. These properties are largely destroyed in a realistic situation when rotations are included. Nevertheless, our analysis of the idealised case is of interest because it may possibly be realised using quantum dots as artificial atoms.Comment: 5 figures; references added, outlook section reduce

Reactive vaccination as a control strategy for pneumococcal meningitis outbreaks in the African meningitis belt: analysis of outbreak data from Ghana

Streptococcus pneumoniae is increasingly recognised as an important cause of bacterial meningitis in the African meningitis belt. The World Health Organization sets guidelines for response to outbreaks of meningococcal meningitis, but there are no current guidelines for outbreaks where S. pneumoniae is implicated. We aimed to evaluate the impact of using a similar response to target outbreaks of vaccine-preventable pneumococcal meningitis in the meningitis belt. Here, we adapt a previous model of reactive vaccination for meningococcal outbreaks to estimate the potential impact of reactive vaccination in a recent pneumococcal meningitis outbreak in the Brong-Ahafo region of central Ghana using weekly line list data on all suspected cases over a period of five months. We determine the sensitivity and specificity of various epidemic thresholds and model the cases and deaths averted by reactive vaccination. An epidemic threshold of 10 suspected cases per 100,000 population per week performed the best, predicting large outbreaks with 100% sensitivity and more than 85% specificity. In this outbreak, reactive vaccination would have prevented a lower number of cases per individual vaccinated (approximately 15,300 doses per case averted) than previously estimated for meningococcal outbreaks. Since the burden of death and disability from pneumococcal meningitis is higher than that from meningococcal meningitis, there may still be merit in considering reactive vaccination for outbreaks of pneumococcal meningitis. More outbreak data are needed to refine our model estimates. Whatever policy is followed, we emphasize the importance of timely laboratory confirmation of suspected cases to enable appropriate decisions about outbreak response.LVC is supported by a studentship from Trinity Hall College

Solutions for the General, Confluent and Biconfluent Heun equations and their connection with Abel equations

In a recent paper, the canonical forms of a new multi-parameter class of Abel differential equations, so-called AIR, all of whose members can be mapped into Riccati equations, were shown to be related to the differential equations for the hypergeometric 2F1, 1F1 and 0F1 functions. In this paper, a connection between the AIR canonical forms and the Heun General (GHE), Confluent (CHE) and Biconfluent (BHE) equations is presented. This connection fixes the value of one of the Heun parameters, expresses another one in terms of those remaining, and provides closed form solutions in terms of pFq functions for the resulting GHE, CHE and BHE, respectively depending on four, three and two irreducible parameters. This connection also turns evident what is the relation between the Heun parameters such that the solutions admit Liouvillian form, and suggests a mechanism for relating linear equations with N and N-1 singularities through the canonical forms of a non-linear equation of one order less.Comment: Original version submitted to Journal of Physics A: 16 pages, related to math.GM/0002059 and math-ph/0402040. Revised version according to referee's comments: 23 pages. Sign corrected (June/17) in formula (79). Second revised version (July/25): 25 pages. See also http://lie.uwaterloo.ca/odetools.ht

Asymptotic Spectroscopy of Rotating Black Holes

We calculate analytically the transmission and reflection amplitudes for waves incident on a rotating black hole in d=4, analytically continued to asymptotically large, nearly imaginary frequency. These amplitudes determine the asymptotic resonant frequencies of the black hole, including quasinormal modes, total-transmission modes and total-reflection modes. We identify these modes with semiclassical bound states of a one-dimensional Schrodinger equation, localized along contours in the complexified r-plane which connect turning points of corresponding null geodesics. Each family of modes has a characteristic temperature and chemical potential. The relations between them provide hints about the microscopic description of the black hole in this asymptotic regime.Comment: References adde

Clustered lot quality assurance sampling: a tool to monitor immunization coverage rapidly during a national yellow fever and polio vaccination campaign in Cameroon, May 2009

We used the clustered lot quality assurance sampling (clustered-LQAS) technique to identify districts with low immunization coverage and guide mop-up actions during the last 4 days of a combined oral polio vaccine (OPV) and yellow fever (YF) vaccination campaign conducted in Cameroon in May 2009. We monitored 17 pre-selected districts at risk for low coverage. We designed LQAS plans to reject districts with YF vaccination coverage <90% and with OPV coverage <95%. In each lot the sample size was 50 (five clusters of 10) with decision values of 3 for assessing OPV and 7 for YF coverage. We ‘rejected' 10 districts for low YF coverage and 14 for low OPV coverage. Hence we recommended a 2-day extension of the campaign. Clustered-LQAS proved to be useful in guiding the campaign vaccination strategy before the completion of the operation

Coherent Excitation of a Two-Level Atom driven by a far off-resonant Classical Field: Analytical Solutions

We present an analytical treatment of coherent excitation of a Two-Level Atom driven by a far-off resonant classical field. A class of pulse envelope is obtained for which this problem is exactly solvable. The solutions are given in terms of Heun function which is a generalization of the Hypergeometric function. The degeneracy of Heun to Hypergeometric equation can give all the exactly solvable pulse shapes of Gauss Hypergeometric form, from the generalized pulse shape obtained here. We discuss the application of the results obtained to the generation of XUV.Comment: 9 Pages, 8 Figures. Accepted for Physical Review A as a regular articl