1,330 research outputs found
Scattering in three-dimensional fuzzy space
We develop scattering theory in a non-commutative space defined by a
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 -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 -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
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