639 research outputs found
Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space
We solve explicitly the two-dimensional harmonic oscillator and the harmonic
oscillator in a background magnetic field in noncommutative phase-space without
making use of any type of representation. A key observation that we make is
that for a specific choice of the noncommutative parameters, the time reversal
symmetry of the systems get restored since the energy spectrum becomes
degenerate. This is in contrast to the noncommutative configuration space where
the time reversal symmetry of the harmonic oscillator is always broken.Comment: 7 pages Late
Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
In analogy with conventional quantum mechanics, non-commutative quantum
mechanics is formulated as a quantum system on the Hilbert space of
Hilbert-Schmidt operators acting on non-commutative configuration space. It is
argued that the standard quantum mechanical interpretation based on Positive
Operator Valued Measures, provides a sufficient framework for the consistent
interpretation of this quantum system. The implications of this formalism for
rotational and time reversal symmetry are discussed. The formalism is applied
to the free particle and harmonic oscillator in two dimensions and the physical
signatures of non commutativity are identified.Comment: 11 page
Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane
The ordinary Landau problem of a charged particle in a plane subjected to a
perpendicular homogeneous and static magnetic field is reconsidered from
different points of view. The role of phase space canonical transformations and
their relation to a choice of gauge in the solution of the problem is
addressed. The Landau problem is then extended to different contexts, in
particular the singular situation of a purely linear potential term being added
as an interaction, for which a complete purely algebraic solution is presented.
This solution is then exploited to solve this same singular Landau problem in
the half-plane, with as motivation the potential relevance of such a geometry
for quantum Hall measurements in the presence of an electric field or a
gravitational quantum well
The N=1 Supersymmetric Landau Problem and its Supersymmetric Landau Level Projections: the N=1 Supersymmetric Moyal-Voros Superplane
The N=1 supersymmetric invariant Landau problem is constructed and solved. By
considering Landau level projections remaining non trivial under N=1
supersymmetry transformations, the algebraic structures of the N=1
supersymmetric covariant non(anti)commutative superplane analogue of the
ordinary N=0 noncommutative Moyal-Voros plane are identified
Noncommutative quantum mechanics -- a perspective on structure and spatial extent
We explore the notion of spatial extent and structure, already alluded to in
earlier literature, within the formulation of quantum mechanics on the
noncommutative plane. Introducing the notion of average position and its
measurement, we find two equivalent pictures: a constrained local description
in position containing additional degrees of freedom, and an unconstrained
nonlocal description in terms of the position without any other degrees of
freedom. Both these descriptions have a corresponding classical theory which
shows that the concept of extended, structured objects emerges quite naturally
and unavoidably there. It is explicitly demonstrated that the conserved energy
and angular momentum contain corrections to those of a point particle. We argue
that these notions also extend naturally to the quantum level. The local
description is found to be the most convenient as it manifestly displays
additional information about structure of quantum states that is more subtly
encoded in the nonlocal, unconstrained description. Subsequently we use this
picture to discuss the free particle and harmonic oscillator as examples.Comment: 25 pages, no figure
Voros product and the Pauli principle at low energies
Using the Voros star product, we investigate the status of the two particle
correlation function to study the possible extent to which the previously
proposed violation of the Pauli principle may impact at low energies. The
results show interesting features which are not present in the computations
made using the Moyal star product.Comment: 5 pages LateX, minor correction
Constraints to the sustainability of a ‘systematised’ approach to livestock marketing amongst smallholder cattle producers in South Africa
Commercialization of smallholder agriculture in South Africa is underpinned by reforms to improve livestock off-take in communal areas and engage smallholder farmers with formal markets. To achieve this, Custom Feeding Programmes (CFPs) were established to improve the condition of communal cattle prior to their sale into formal markets and to ‘systematise’ the informal marketing of cattle in communal areas by enabling participants to achieve higher informal market prices. We evaluate the sustainability of eight CFPs located in Eastern Cape Province in terms of their ability to add value to smallholder cattle production and encourage market participation. Communities with CFPs achieved a 16.6% mean cattle off-take rate, substantially higher than in most communal systems. Furthermore, cattle sold through CFPs attained a 17% higher mean selling price than those sold through other marketing channels. However, these benefits were mainly realized by better-off farmers with larger cattle herds and greater ability to transport animals to and from CFPs. More marginalized farmers, particularly women, had low participation. CFPs also face challenges to their sustainability, including inconsistent feed and water supplies, poor infrastructure and high staff turnover. Key to enhancing participation in CFPs, will be improving the way they are supported and embedded within communities
Shell-model calculations for the three-nucleon system
We use Faddeev's decomposition to solve the shell-model problem for three
nucleons. The dependence on harmonic-oscillator excitations allowed in the
model space, up to in the present calculations, and on the
harmonic-oscillator frequency is studied. Effective interactions derived from
Nijmegen II and Reid93 potentials are used in the calculations. The binding
energies obtained are close to those calculated by other methods. The structure
of the Faddeev equations is discussed and a simple formula for matrix elements
of the permutation operators in a harmonic-oscillator basis is given. The Pauli
principle is properly treated in the calculations.Comment: 11 pages. REVTEX. 6 PostScript figure
A (p,q)-deformed Landau problem in a spherical harmonic well: spectrum and noncommuting coordinates
A (p,q)-deformation of the Landau problem in a spherically symmetric harmonic
potential is considered. The quantum spectrum as well as space noncommutativity
are established, whether for the full Landau problem or its quantum Hall
projections. The well known noncommutative geometry in each Landau level is
recovered in the appropriate limit p,q=1. However, a novel noncommutative
algebra for space coordinates is obtained in the (p,q)-deformed case, which
could also be of interest to collective phenomena in condensed matter systems.Comment: 9 pages, no figures; updated reference
Experimental evidence of non-Amontons behaviour at a multicontact interface
We report on normal stress field measurements at the multicontact interface
between a rough elastomeric film and a smooth glass sphere under normal load,
using an original MEMS-based stress sensing device. These measurements are
compared to Finite Elements Method calculations with boundary conditions
obeying locally Amontons' rigid-plastic-like friction law with a uniform
friction coefficient. In dry contact conditions, significant deviations are
observed which decrease with increasing load. In lubricated conditions, the
measured profile recovers almost perfectly the predicted profile. These results
are interpreted as a consequence of the finite compliance of the multicontact
interface, a mechanism which is not taken into account in Amontons' law
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