Observation of Exceptional Points in Electronic Circuits

Two damped coupled oscillators have been used to demonstrate the occurrence of exceptional points in a purely classical system. The implementation was achieved with electronic circuits in the kHz-range. The experimental results perfectly match the mathematical predictions at the exceptional point. A discussion about the universal occurrence of exceptional points -- connecting dissipation with spatial orientation -- concludes the paper.Comment: 4 pages, latex, 3 postscript figures, submitted for publicatio

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

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

An Unfolded Quantization for Twisted Hopf Algebras

In this talk I discuss a recently developed "Unfolded Quantization Framework". It allows to introduce a Hamiltonian Second Quantization based on a Hopf algebra endowed with a coproduct satisfying, for the Hamiltonian, the physical requirement of being a primitive element. The scheme can be applied to theories deformed via a Drinfeld twist. I discuss in particular two cases: the abelian twist deformation of a rotationally invariant nonrelativistic Quantum Mechanics (the twist induces a standard noncommutativity) and the Jordanian twist of the harmonic oscillator. In the latter case the twist induces a Snyder non-commutativity for the space-coordinates, with a pseudo-Hermitian deformed Hamiltonian. The "Unfolded Quantization Framework" unambiguously fixes the non-additive effective interactions in the multi-particle sector of the deformed quantum theory. The statistics of the particles is preserved even in the presence of a deformation.Comment: 9 pages. Talk given at QTS7 (7th Int. Conf. on Quantum Theory and Symmetries, Prague, August 2011

Book Reviews

Book Review 1Book Title: The Physiology of ReproductionBook Authors: Editors-in-Chief: E. Knobil, & J.D. KneillRaven Press, 1988. 2633 pagesBook Review 2Book Title: Long-term Studies in Ecology: Approaches and AlternativesBook Author: Gene E. LikensSpringer-Verlag, New York, 1988. 214 pages, 27 figures. ISBN 3-540-96743-5.Book Review 3Book Title: Oceans of Life off Southern AfricaBook Authors: Edited by Andrew I.L. Payne & Robert J.M. Crawford and illustrated by Anthony P. van DalsenVlaeberg Publishers, Cape Town, 1989. 300 pp., numerous figures, tables and photographs.Book Review 4Book Title: Biotic Diversity in Southern Africa: Concepts and ConservationBook Author: Edited by B.J. HuntleyOxford University Press, Cape Town, 1989. 380 pages, hardback edition.Book Review 5Book Title: Ecosystems of the World 14B, Tropical Rain Forest Ecosystems: Biogeographical and Ecological StudiesBook Authors: Edited by H. Leith & M.J.A. WergerElsevier, 1989

Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem

In a previous paper (arXiv:math-ph/0604055) we introduced a very simple PT-symmetric non-Hermitian Hamiltonian with real spectrum and derived a closed formula for the metric operator relating the problem to a Hermitian one. In this note we propose an alternative formula for the metric operator, which we believe is more elegant and whose construction -- based on a backward use of the spectral theorem for self-adjoint operators -- provides new insights into the nature of the model.Comment: LaTeX, 6 page

Testing earthquake links in Mexico from 1978 to the 2017 M = 8.1 Chiapas and M = 7.1 Puebla Shocks

The M = 8.1 Chiapas and the M = 7.1 Puebla earthquakes occurred in the bending part of the subducting Cocos plate 11 days and ~600 km apart, a range that puts them well outside the typical aftershock zone. We find this to be a relatively common occurrence in Mexico, with 14% of M > 7.0 earthquakes since 1900 striking more than 300 km apart and within a 2 week interval, not different from a randomized catalog. We calculate the triggering potential caused by crustal stress redistribution from large subduction earthquakes over the last 40 years. There is no evidence that static stress transfer or dynamic triggering from the 8 September Chiapas earthquake promoted the 19 September earthquake. Both recent earthquakes were promoted by past thrust events instead, including delayed afterslip from the 2012 M = 7.5 Oaxaca earthquake. A repeated pattern of shallow thrust events promoting deep intraslab earthquakes is observed over the past 40 years

Strings from position-dependent noncommutativity

We introduce a new set of noncommutative space-time commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative space-time relations taken here to have position dependent structure constants. Some of the new variables are non-Hermitian in the most natural choice. We construct their Hermitian counterparts by means of a Dyson map, which also serves to introduce a new metric operator. We propose PTlike symmetries, i.e.antilinear involutory maps, respected by these deformations. We compute minimal lengths and momenta arising in this space from generalized versions of Heisenberg's uncertainty relations and find that any object in this two dimensional space is string like, i.e.having a fundamental length in one direction beyond which a resolution is impossible. Subsequently we formulate and partly solve some simple models in these new variables, the free particle, its PT-symmetric deformations and the harmonic oscillator.Comment: 11 pages, Late

Coherent States on Hilbert Modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert $C^*$-modules which have a natural left action from another $C^*$-algebra say, $\mathcal A$. The coherent states are well defined in this case and they behave well with respect to the left action by $\mathcal A$. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive kernel between two $C^*$-algebras, in complete analogy to the Hilbert space situation. Related to this there is a dilation result for positive operator valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory

Cu Nuclear Quadrupole Resonance Study of Site-Disorder and Chemical Pressure Effects on Y(Ba1-xSrx)2Cu4O8

We report a zero-field Cu nuclear quadrupole resonance (NQR) study on the effects of nonmagnetic Sr substitution for high-Tc superconductors, Y(Ba1-xSrx)2Cu4O8 (Tc=82-80 K for x=0-0.4), using a spin-echo technique. The site-disordering and chemical pressure effects associated with doping Sr were observed in the broadened, shifted Cu NQR spectra. Nevertheless, the site disorder did not significantly affect the homogeneity of Cu electron spin dynamics, in contrast to the in-plane impurity. The peak shift of Cu NQR spectrum due to Sr was different between the chain- and the plane-Cu sites, more remarkably than those under a hydrostatic physical pressure, suggesting anisotropic or nonuniform local structural strains. The small decrease of Tc due to Sr can be traced back to either a cancellation effect on Tc between the disorder and the pressure, or an anisotropic or nonuniform chemical pressure effect on Tc.Comment: 4 pages, 5 figure