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

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

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 asymptotically flat solutions of Einstein's equations periodic in time I. Vacuum and electrovacuum solutions

By an argument similar to that of Gibbons and Stewart, but in a different coordinate system and less restrictive gauge, we show that any weakly-asymptotically-simple, analytic vacuum or electrovacuum solutions of the Einstein equations which are periodic in time are necessarily stationary.Comment: 25 pages, 2 figures, published in Class. Quant. Grav

Solvable relativistic quantum dots with vibrational spectra

For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where spectrum is roughly equidistant and where a fine-tuning of the levels is mediated by PT-symmetric interactions composed of imaginary delta functions which mimic creation/annihilation processes.Comment: Int. Worskhop "Pseudo-Hermitian Hamiltonians in Quantum Physics III" (June 20 - 22, 2005, Koc Unversity, Istanbul(http://home.ku.edu.tr/~amostafazadeh/workshop/workshop.htm) a part of talk (9 pages

Moyal products -- a new perspective on quasi-hermitian quantum mechanics

The rationale for introducing non-hermitian Hamiltonians and other observables is reviewed and open issues identified. We present a new approach based on Moyal products to compute the metric for quasi-hermitian systems. This approach is not only an efficient method of computation, but also suggests a new perspective on quasi-hermitian quantum mechanics which invites further exploration. In particular, we present some first results which link the Berry connection and curvature to non-perturbative properties and the metric.Comment: 14 pages. Submitted to J Phys A special issue on The Physics of Non-Hermitian Operator

Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations

The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\cal PT$-symmetric part, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it opens the way towards the construction of generalized non-Hermitian (not necessarily $\cal PT$-symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.Comment: 11 pages, no figure; changes in title and in paragraphs 3 and 5; final published versio

Impact of ownership structure along the value chain in the manufacturing business

In the chemical and petrochemical industry, it is quite common that the manufacturing of a final product is the result of several consecutive steps which can be owned and operated by one or many participants. Although not always practical, equal ownership among all partners along the value chain is often recommended as a way to simplify business structure, ensuring all partners share equally in the ups and downs of an uncertain market. In contrast to this approach, there are instances where more benefit can be derived from having different owners and operators along the value chain. Examples which are common practice in the industry are the supply of utilities (e.g., electricity), feedstock, and services. In these cases, the nonintegrated approach offers value as: It provides the operator of the upstream or utility plants the opportunity to specialize, for example, by operating very similar plants around the world. Such specialization enables the use of regional operating centers, minimum onsite cash costs, optimized operating conditions, minimized energy consumption, and the optimal use of other variable cost parameters. This article shows that if outsourcing results in a cash cost saving by an upstream operator, the benefit to the downstream owner will (in financial reward) be proportional to the cash cost saving achieved. In absolute terms, the magnitude of the benefit is moderated by the size of the downstream capital investment (The bigger the downstream investment relative to the upstream investment, the smaller the impact of the saving on the economics of the downstream company). As a “utility provider” an upstream operator benefits from lower risk in terms of offtake and market price uncertainties. Such owners benefit from a lower cost of capital, and as such also have lower return expectations than players further along in the value chain (who are exposed to all the uncertainties in volatile markets). This article shows that the positive impact of such benefits to the return of the downstream partner is directly proportional the difference in return expectations between the upstream and downstream company. Once again, the absolute magnitude of the saving becomes more substantial as the ratio of upstream capital investment increases relative to the downstream capital investment. Economy of learning may also enable a specialized upstream company to obtain an asset at a lower capital than a less specialized downstream operator. This article shows that the positive impact of such a benefit is very similar to that of a lower return expectation by the upstream company.http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1547-59052017-04-30hb2016Chemical Engineerin

The higher classification of southern African insects

A number of changes have taken place in the higher classification of southern African insects since the last time it was documented in full (Scholtz & Holm 1985) and there is currently no comprehensive modern classification of higher insect taxa available for the region.http://reference.sabinet.co.za/sa_epublication/entohttp://www.entsocsa.co.za/Publications.htm2018-09-30am2016Zoology and Entomolog