Absence of an intrinsic value for the surface recombination velocity in doped semiconductors

A self-consistent expression for the surface recombination velocity $S$ and the surface Fermi level unpinning energy as a function of light excitation power ($P$) is presented for n- and p-type semiconductors doped above the 10$^{16}$ cm$^{-3}$ range. Measurements of $S$ on p-type GaAs films using a novel polarized microluminescence technique are used to illustrate two limiting cases of the model. For a naturally oxidized surface $S$ is described by a power law in $P$ whereas for a passivated surface $S^{-1}$ varies logarithmically with $P$. Furthermore, the variation in $S$ with surface state density and bulk doping level is found to be the result of Fermi level unpinning rather than a change in the intrinsic surface recombination velocity. It is concluded that $S$ depends on $P$ throughout the experimentally accessible range of excitation powers and therefore that no instrinsic value can be determined. Previously reported values of $S$ on a range of semiconducting materials are thus only valid for a specific excitation power.Comment: 10 pages, 7 figure

Ince's limits for confluent and double-confluent Heun equations

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable $z$, while the other is given by a series of modified Bessel functions and converges for $|z|>|z_{0}|$, where $z_{0}$ denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when $z_{0}$ tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schr\"odinger equation for inverse fourth and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.Comment: Submitted to Journal of Mathmatical Physic

A Note on Tachyons in the D3+D3ˉD3+{\bar {D3}} System

The periodic bounce of Born-Infeld theory of $D3$-branes is derived, and the BPS limit of infinite period is discussed as an example of tachyon condensation. The explicit bounce solution to the Born--Infeld action is interpreted as an unstable fundamental string stretched between the brane and its antibrane.Comment: 10 pages, 2 figures. v2: minor changes, acknowledgement added; v3: explanations and references added. Final version to appear in Mod. Phys. Lett.

Discrete spectra for confined and unconfined -a/r + b r^2 potentials in d dimensions

Exact solutions to the d-dimensional Schroedinger equation, d\geq 2, for Coulomb plus harmonic oscillator potentials V(r)=-a/r+br^2, b>0 and a\ne 0 are obtained. The potential V(r) is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical box of radius R. With the aid of the asymptotic iteration method, the exact analytic solutions under certain constraints, and general approximate solutions, are obtained. These exhibit the parametric dependence of the eigenenergies on a, b, and R. The wave functions have the simple form of a product of a power function, an exponential function, and a polynomial. In order to achieve our results the question of determining the polynomial solutions of the second-order differential equation (\sum_{i=0}^{k+2}a_{k+2,i}r^{k+2-i})y"+(\sum_{i=0}^{k+1}a_{k+1,i}r^{k+1-i})y'-(\sum_{i=0}^{k}\tau_{k,i}r^{k-i})y=0 for k=0,1,2 is solved.Comment: 16 pages, 1 figur

Quasi-Exact Solvability and the direct approach to invariant subspaces

We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: an interesting generalization of the Lam\'e potential which posses four algebraic sectors, and a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic.Comment: 17 pages, 3 figure

Spiked oscillators: exact solution

A procedure to obtain the eigenenergies and eigenfunctions of a quantum spiked oscillator is presented. The originality of the method lies in an adequate use of asymptotic expansions of Wronskians of algebraic solutions of the Schroedinger equation. The procedure is applied to three familiar examples of spiked oscillators

Fifth-year medical students’ perspectives on rural training in Botswana: A qualitative approach

Background. The curriculum of the Faculty of Medicine at the University of Botswana includes rural community exposure for students throughout their 5 years of training. In addition to community exposure during the first 2 years, students complete 16 weeks of family medicine and 8 weeks of public health medicine. However, as a new faculty, students’ experiences and perceptions regarding rural clinical training are not yet known.Objective. To describe the experiences and perceptions of the 5th-year medical students during their rural training and solicit their recommendations for improvement.Methods. This qualitative study used face-to-face interviews with 5th-year undergraduate medical students (N=36) at the end of their family medicine rotation in Mahalapye and Maun villages. We used a phenomenological paradigm to underpin the study. Voice-recorded interviews were transcribed and analysed using Atlas TI version 7 software (USA).Results. Three main themes were identified: (i) experiences and perceptions of the rural training environment; (ii) perceptions of the staff at rural sites; and (iii) perceptions of clinical benefits and relevance during rural training. While the majority of students perceived rural training as beneficial and valuable, a few felt that learning was compromised by limited resources and processes, such as medical equipment, internet connectivity and inadequate supervision.Conclusion. While the majority of students perceived rural training as beneficial, students identified limitations in both resources and supervision that need to be improved. Understanding students’ rural training experiences and perceptions can help the Faculty of Medicine, stakeholders and site facilitators to guide future rural training implementation

Tachyon condensation on brane sphalerons

We consider a sphaleron solution in field theory that provides a toy model for unstable D-branes of string theory. We investigate the tachyon condensation on a Dp-brane. The localized modes, including a tachyon, arise in the spectrum of a sphaleron solution of a \phi^4 field theory on M^{p+1}\times S^1. We use these modes to find a multiscalar tachyon potential living on the sphaleron world-volume. A complete cancelation between brane tension and the minimum of the tachyon potential is found as the size of the circle becomes small.Comment: To appear in JHEP, 13 pages, 2 eps figures, minor changes and references adde