The five-dimensional Kepler Problem as an SU(2) Gauge System: Algebraic Constraint Quantization

Starting from the structural similarity between the quantum theory of gauge systems and that of the Kepler problem, an SU(2) gauge description of the five-dimensional Kepler problem is given. This non-abelian gauge system is used as a testing ground for the application of an algebraic constraint quantization scheme which can be formulated entirely in terms of observable quantities. For the quantum mechanical reduction only the quadratic Casimir of the constraint algebra, interpreted as an observable, is needed.Comment: 29 pages, Latex, no figure

Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn x

We consider a singular Sturm-Liouville expression with the indefinite weight sgn x. To this expression there is naturally a self-adjoint operator in some Krein space associated. We characterize the local definitizability of this operator in a neighbourhood of $\infty$. Moreover, in this situation, the point $\infty$ is a regular critical point. We construct an operator A=(\sgn x)(-d^2/dx^2+q) with non-real spectrum accumulating to a real point. The obtained results are applied to several classes of Sturm-Liouville operators.Comment: 21 pages, LaTe

On Domains of PT Symmetric Operators Related to -y''(x) + (-1)^n x^{2n}y(x)

In the recent years a generalization of Hermiticity was investigated using a complex deformation H=p^2 +x^2(ix)^\epsilon of the harmonic oscillator Hamiltonian, where \epsilon is a real parameter. These complex Hamiltonians, possessing PT symmetry (the product of parity and time reversal), can have real spectrum. We will consider the most simple case: \epsilon even. In this paper we describe all self-adjoint (Hermitian) and at the same time PT symmetric operators associated to H=p^2 +x^2(ix)^\epsilon. Surprisingly it turns out that there are a large class of self-adjoint operators associated to H=p^2 +x^2(ix)^\epsilon which are not PT symmetric

Ensuring Professionalism of the External Evaluation Commission: The Slovenian Case Study

In 2006–2007, the Slovenian higher education (HE) system took the first steps toward building a national model of institutional external evaluation (IEE), which would be comparable with other European models. In the first part of the article, the authors discuss the main tendencies within the European he area. This is followed by an outline of the developments in the field of quality assurance within Slovenian he, stressing the years 2006 and 2007. The scientific contribution of the article lies in the evaluation outcomes of the national pilot IEES, with focus on the professional competences of the External evaluation commission (EEC) members. Observation results stress the importance of the proper training of EEC members. The authors propose that a systematic follow-up on the EEC work needs to be established and a code of ethics drawn up, highlighting the preferred values and principles of EEC members.quality assurance, higher education, external evaluation, institutional evaluation, external evaluation commission

Novel ZnO-based Ternary Oxides for Optoelectronic Applications

Zinc oxide (ZnO) has been used in a wide range of products for many years, including, among others, varistors, surface acoustic wave devices and cosmetics. Besides these established applications, ZnO and its ternary alloys are now also being considered as potential materials for optoelectronic applications, such as light emitting diodes, photovoltaics, sensors, displays, etc. Unlike other materials, which could be used alternatively, ZnO has the advantage of being inexpensive, chemically stable and relatively plentiful. In spite of the long research history, fabrication of defect free ternary alloys and stable p-type ZnO is still challenging. The aim of this work was therefore to provide a better understanding of ZnO ternary alloys, so that - based on the gained knowledge - their optical properties can be further improved and, in a second step, optoelectronic applications based on these materials can soon be commercialized. The work carried out in this thesis was two-fold: the first part aimed at identifying the origin of defect related luminescence phenomena in ZnMgO, and the second part was dedicated to the exploration of a novel ZnCdO-based heterostructure photovoltaic applications. In the case of ZnMgO, luminescence properties of deep level defects were studied by photoluminescence (PL) spectroscopy and a model was proposed to explain the changes in the deep band emission with increasing Mg content. In this model, the observed trends can be understood by considering interaction of native zinc and oxygen defects of the ZnO sublattice with Mg interstitials (Mgi). In summary, the deep level bands at 3.0 and 2.8 eV, which show a blueshift with increasing Mg content, were assigned to free-to-bound type transitions between zinc interstitials (Zni) with the valence band edge and between the conduction band edge with zinc vacancies (VZn), respectively. A red band at 2.0 eV, which does not show an apparent shift of the peak energy for increasing Mg content, is associated with the oxygen vacancies (VO). Two luminescence bands at 2.3 and 2.5 eV, which are redshifted for higher Mg concentrations, were assigned to transitions between zinc and oxygen interstitials and between zinc interstitials and zinc vacancies, respectively. The redshift is interpreted in terms of a competing supply of electrons from slightly deeper Mgi donor states. The ZnMgO band gap diagram, which the model is based on, has contributed to gain valuable information about the nature of the deep defects both in ZnO and ZnMgO and is therefore of fundamental interest. In the second part of this work, focused on ZnCdO, a stacked heterostructure was designed for application in a photoelectrochemical cell, which is used for hydrogen production by photoelectrolysis using the semiconductor as an absorber. Optical and photoelectrochemical measurements led to the conclusion that the optical emission band for the ZnCdO heterostructures is broadened compared to a ZnO single layer. The broadened emission could be explained by combined excitonic recombination from the individual layers in the structure. The carrier dynamics in the structures were further investigated by time-resolved photoluminescence spectroscopy. A comparison of recombination parameters in ZnCdO heterostructures and in ZnO single layer films suggests a higher density of non-radiative recombination centers in the heterostructures. Furthermore, the effect of built-in fields on the carrier dynamics was assessed by investigating carrier recombination processes in a variety of different heterostructure geometries. The study does not only provide knowledge necessary to understand the origin of limiting factors in the proposed ZnCdO structure, but is also of general interest as the insight can be applied to a variety of other graded band gap type structures. Finally, photoelectrochemical testing of the ZnCdO structures confirmed the optical activity of the films, thus providing a proof of concept for the suitability of ZnCdO heterostructures as photoanodes in photoelectrochemical cells

Numerical Range and Quadratic Numerical Range for Damped Systems

We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations $\ddot{z}(t) + D \dot{z} (t) + A_0 z(t) = 0$ in a Hilbert space. Our main tool is the quadratic numerical range for which we establish the spectral inclusion property under weak assumptions on the operators involved; in particular, the damping operator only needs to be accretive and may have the same strength as $A_0$. By means of the quadratic numerical range, we establish tight spectral estimates in terms of the unbounded operator coefficients $A_0$ and $D$ which improve earlier results for sectorial and selfadjoint $D$; in contrast to numerical range bounds, our enclosures may even provide bounded imaginary part of the spectrum or a spectral free vertical strip. An application to small transverse oscillations of a horizontal pipe carrying a steady-state flow of an ideal incompressible fluid illustrates that our new bounds are explicit.Comment: 27 page