Eigenvalue distributions from a star product approach

We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is based on the $su(2)$ coherent states which allow for a systematic 1/D expansion of the star product. This produces a trace formula for functions of the matrix sequence elements in the large-$D$ limit which includes higher order (finite-$D$) corrections. From this a variety of analytic results pertaining to the asymptotic properties of the density of states, eigenstates and expectation values associated with the matrix sequence follows. It is shown how new and existing results in the settings of collective spin systems and orthogonal polynomial sequences can be readily obtained as special cases. In particular, this approach allows for the calculation of higher order corrections to the zero distributions of a large class of orthogonal polynomials.Comment: 25 pages, 8 figure

Scattering in three-dimensional fuzzy space

We develop scattering theory in a non-commutative space defined by a $su(2)$ coordinate algebra. By introducing a positive operator valued measure as a replacement for strong position measurements, we are able to derive explicit expressions for the probability current, differential and total cross-sections. We show that at low incident energies the kinematics of these expressions is identical to that of commutative scattering theory. The consequences of spacial non-commutativity are found to be more pronounced at the dynamical level where, even at low incident energies, the phase shifts of the partial waves can deviate strongly from commutative results. This is demonstrated for scattering from a spherical well. The impact of non-commutativity on the well's spectrum and on the properties of its bound and scattering states are considered in detail. It is found that for sufficiently large well-depths the potential effectively becomes repulsive and that the cross-section tends towards that of hard sphere scattering. This can occur even at low incident energies when the particle's wave-length inside the well becomes comparable to the non-commutative length-scale.Comment: 12 pages, 6 figure

Nutritional management of encapsulating peritoneal sclerosis with intradialytic parenteral nutrition

No Abstract

Duality constructions from quantum state manifolds

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS_2/CFT_1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et. al. the corresponding state manifold is seen to be exactly AdS_2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.Comment: 25 Pages, References Adde

Synthesis and Antitumour Activity of Gold(I) and Silver(I) Complexes of Hydrazine-Bridged Diphosphine Ligands

A known synthetic route was used to prepare two known hydrazine-bridged phosphine ligands and four new ligands with variable groups on the hydrazine bridge (methyl and ethyl), as well as positions on the aryl phosphine groups (phenyl, methoxyphenyl, dimethylaminophenyl). A range of gold(I) and silver(I) complexes were synthesized utilizing these phosphine ligands. Both the phosphine-bridged dimetal and cationic bis(diphosphine) metal complexes were isolated. An interesting phenomenon of the spontaneous oxidation of gold(I) to gold(III) (and reduction of gold(IIII) to gold(I)) upon complexation with ((N,N-dimethyl)-4-aminophenyl)dialkylhydrazine ligands is described. Thirteen of the synthesized complexes were subjected to anticancer activity screening against HeLa, Jurkat, A2780, cisplatin-resistant A2780, CoLo 320 DM and MCF7. Most of the complexes were found to inhibit the cancerous cells at low μM concentrations and in some cases nM concentrations. Two of the complexes were tested for their ability to reduce the mitochondrial membrane potential ofPBMCcells as a possible mechanism of action of anticancer activity.Keywords: Gold(I), silver(I), hydrazine, diphosphine, antitumour, anticancer, mitochondrial membrane potentia

Spectrum of the three dimensional fuzzy well

We develop the formalism of quantum mechanics on three dimensional fuzzy space and solve the Schr\"odinger equation for a free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits. A high energy cut-off is found for the free particle spectrum, which also results in the modification of the high energy dispersion relation. An ultra-violet/infra-red duality is manifest in the free particle spectrum. The finite well also has an upper bound on the possible energy eigenvalues. The phase shifts due to scattering around the finite fuzzy potential well have been calculated

On the Thermodynamic Limit of the Lipkin Model

The thermodynamic limit of the Lipkin model is investigated. While the limit turns out to be rather elusive, the analysis gives strong indications that the limit yields two analytically dissociated operators, one for the normal and one for the deformed phase. While the Lipkin Hamiltonian is hermitian and has a second order phase transition in finite dimensions (finite particle number), both properties seem to be destroyed in the thermodynamic limit.Comment: 9 pages, 3 figures to appear in JPhys

Determining the elements of the operations management transformation model for the monitoring and breaching of the Great Brak River Mouth system

The prime challenge to those responsible for the management of South Africa’s estuaries is to maintain their viability in the face of ever increasing pressures. It is important that we learn to appreciate the value of estuaries and that we act wisely to manage them for sustainable use. Any operation must have the adequate resources to perform the duties and the correct processes must be followed. The purpose of this research is to determine whether the current inputs and processes needed for the monitoring and breaching of the Great Brak River Mouth system are sufficient to adhere to the output objectives of a healthy estuary together with safeguarding of properties. The research methodology for this study comprised the following steps: Firstly, a literature study was performed to identify the key elements of the operation management transformation model. Operations management deals with the output of any business, in other words the conversion of inputs to create certain outputs and they do this by a process of transformation. Secondly, extensive literature study was performed in order to access material regarding effective estuary and river mouth management. Thirdly, the current situation at Great Brak was assessed to determine whether the current inputs and processes are in place and if additional or altered inputs and processes are needed