Foldy-Wouthuysen Transformation, Scalar Potentials and Gravity

We show that care is required in formulating the nonrelativistic limit of generalized Dirac Hamiltonians which describe particles and antiparticles interacting with static electric and/or gravitational fields. The Dirac-Coulomb and the Dirac-Schwarzschild Hamiltonians, and the corrections to the Dirac equation in a non-inertial frame, according to general relativity, are used as example cases in order to investigate the unitarity of the standard and "chiral" approaches to the Foldy-Wouthuysen transformation, and spurious parity-breaking terms. Indeed, we find that parity-violating terms can be generated by unitary pseudo-scalar transformations ("chiral" Foldy-Wouthuysen transformations). Despite their interesting algebraic properties, we find that "chiral" Foldy-Wouthuysen transformations change fundamental symmetry properties of the Hamiltonian and do not conserve the physical interpretation of the operators. Supplementing the discussion, we calculate the leading terms in the Foldy-Wouthuysen transformation of the Dirac Hamiltonian with a scalar potential (of the (1/r)-form and of the confining radially symmetric linear form), and obtain compact expressions for the leading higher-order corrections to the Dirac Hamiltonian in a non-inertial rotating reference frame "Mashhoon term").Comment: 11 pages; RevTe

Dirac Hamiltonian and Reissner-Nordstrom Metric: Coulomb Interaction in Curved Space-Time

We investigate the spin-1/2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordstrom space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordstrom geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational, and electro-gravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electro-gravitational correction terms to the potential proportional to alpha^n G, where alpha is the fine-structure constant, and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.Comment: 11 page

Effects of the topology of social networks on information transmission

Social behaviours cannot be fully understood without considering the network structures that underlie them. Developments in network theory provide us with relevant modelling tools. The topology of social networks may be due to selection for information transmission. To investigate this, we generated network topologies with varying proportions of random connections and degrees of preferential attachment. We simulated two social tasks on these networks: a spreading innovation model and a simple market. Results indicated that non-zero levels of random connections and low levels of preferential attachment led to more efficient information transmission. Theoretical and practical implications are discussed

Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem

We present an intuitive and scalable algorithm for the diagonalization of complex symmetric matrices, which arise from the projection of pseudo--Hermitian and complex scaled Hamiltonians onto a suitable basis set of "trial" states. The algorithm diagonalizes complex and symmetric (non--Hermitian) matrices and is easily implemented in modern computer languages. It is based on generalized Householder transformations and relies on iterative similarity transformations T -> T' = Q^T T Q, where Q is a complex and orthogonal, but not unitary, matrix, i.e, Q^T equals Q^(-1) but Q^+ is different from Q^(-1). We present numerical reference data to support the scalability of the algorithm. We construct the generalized Householder transformations from the notion that the conserved scalar product of eigenstates Psi_n and Psi_m of a pseudo-Hermitian quantum mechanical Hamiltonian can be reformulated in terms of the generalized indefinite inner product [integral of the product Psi_n(x,t) Psi_m(x,t) over dx], where the integrand is locally defined, and complex conjugation is avoided. A few example calculations are described which illustrate the physical origin of the ideas used in the construction of the algorithm.Comment: 14 pages; RevTeX; font mismatch in Eqs. (3) and (15) is eliminate

Social learning mechanisms compared in a simple environment

Social learning can be adaptive, but little is known about the underlying mechanisms. Many researchers have focused on imitation but this may have led to simpler mechanisms being underestimated. We demonstrate in simulation that imitative learning is not always the best strategy for a group-living animal, and that the effectiveness of any such strategy will depend on details of the environment and the animal's lifestyle. We show that observations of behavioural convergence or "traditions" might suggest effective social learning, but are meaningless considered alone

Sexual negotiation in the AIDS era: negotiated safety revisited

Objective: To test the safety of the 'negotiated safety' strategy - the strategy of dispensing with condoms within HIV-seronegative concordant regular sexual relationships under certain conditions. Method: Data from a recently recruited cohort of homosexually active men (Sydney Men and Sexual Health cohort, n = 1037) are used to revisit negotiated safety. The men were surveyed using a structured questionnaire and questions addressing their sexual relationships and practice, their own and their regular partner's serostatus, agreements entered into by the men concerning sexual practice within and outside their regular relationship, and contextual and demographic variables. Results: The findings indicate that a significant number of men used negotiated safety as an HIV prevention strategy. In the 6 months prior to interview, of the 181 men in seroconcordant HIV-negative regular relationships, 62% had engaged in unprotected anal intercourse within their relationship, and 91% (165 men) had not engaged in unprotected anal intercourse outside their relationship. Of these 165 men, 82% had negotiated agreements about sex outside their relationship. The safety of negotiation was dependent not only on seroconcordance but also on the presence of an agreement; 82% of the men who had not engaged in unprotected anal intercourse outside their regular relationship had entered into an agreement with their partner, whereas only 56% of those who had engaged in unprotected anal intercourse had an agreement. The safety of negotiation was also related to the nature of the safety agreement reached between the men and on the acceptability of condoms. Agreements between HIV-negative seroconcordant regular partners prohibiting anal intercourse with casual partners or any form of sex with a casual partner were typically complied with, and men who had such negotiated agreements were at low risk of HIV infection. Conclusions: The adoption of the strategy of negotiated safety among men in HIV-seronegative regular relationships may help such men sustain the safety of their sexual practice

The effects of periodic and continuous market environments on the performance of trading agents

Simulation experiments are conducted on simple continuous double auction (CDA) markets based on the experimental economics work of Vernon Smith. CDA models within experimental economics usually consist of a sequence of discrete trading periods or “days”, with allocations of stock and currency replenished at the start of each day, a situation we call “periodic” replenishment. In our experiments we look at both periodic and continuous-replenishment versions of the CDA. In this we build on the work of Cliff and Preist (2001) with human subjects, but we replace human traders with Zero Intelligence Plus (ZIP) trading agents, a minimal algorithm that can produce equilibrating market behaviour in CDA models. Our results indicate that continuous-replenishment (CR) CDA markets are similar to conventional periodic CDA markets in their ability to show equilibration dynamics. Secondly we show that although both models produce the same behaviour of price formation, they are different playing fields, as periodic markets are more efficient over time than their continuous counterparts. We also find, however, that the volume of trade in periodic CDA markets is concentrated in the early period of each trading day, and the market is in this sense inefficient. We look at whether ZIP agents require different parameters for optimal behaviour in each market type, and find that this is indeed the case. Overall, our conclusions mirror earlier findings on the robustness of the CDA, but we stress that a CR-CDA marketplace equilibrates in a different way to a periodic one

Demography of sea lamprey (Petromyzon marinus) ammocoete populations in relation to potential spawning-migration obstructions

Copyright © 2017 John Wiley & Sons, Ltd. Recent advances in the understanding of lamprey migrations have led to concerns over the impacts of obstructions on the demography of many species. This study investigated sea lamprey (Petromyzon marinus) larvae (ammocoetes) in two adjacent but contrasting rivers, both designated Special Areas of Conservation under the EC Habitats Directive (92/43/EEC), one (the River Wye) with a small number of potential migration obstructions in its upper reaches and one (the River Usk) with obstacles along its course. The geographical distributions, densities and age structures of the ammocoete populations were examined in relation to the locations of potential obstructions to the spawning migrations of anadromous adults. A minimum of three age classes was recorded as far as 200 km upstream of the mouth of the River Wye (93% of the length of the mainstem), demonstrating that adults regularly migrate to the upper reaches of the catchment (downstream of a natural waterfall). By contrast, sea lamprey ammocoetes appeared to be absent (in suitable habitat) from 20 km (17%) of the River Usk, and there was a reduction in density, prevalence and the number of age classes upstream of two putative spawning-migration obstructions. This study highlights some of the potential impacts of habitat fragmentation by obstructions on the spawning migrations of anadromous species, as inferred from ammocoete demography. When used in combination to compare contiguous reaches, ammocoete densities, prevalence and age structure may be a useful indicator of which structures are likely to be important migration obstructions, and where further studies or mitigation efforts should be focused. It is likely that passage past some obstructions is enhanced if high river levels occur during the spawning migration, but there is a need to facilitate passage during all conditions, to improve access to under-exploited spawning and nursery areas

Gravitational Interactions and Fine-Structure Constant

Electromagnetic and gravitational central-field problems are studied with relativistic quantum mechanics on curved space-time backgrounds. Corrections to the transition current are identified. Analogies of the gravitational and electromagnetic spectra suggest the definition of a gravitational fine-structure constant. The electromagnetic and gravitational coupling constants enter the Einstein-Hilbert-Maxwell Lagrangian. We postulate that the variational principle holds with regard to a global dilation transformation of the space-time coordinates. The variation suggests is consistent with a functional relationship of the form alpha_QED being proportional to alpha_G^(1/2), where alpha_QED is the electrodynamic fine-structure constant, and alpha_G its gravitational analogue.Comment: 9 pages; LaTeX; Appeared in the Proceedings to the 17th Bled workshop "What Comes Beyond the Standard Models", Bled, Slovenia, July 2-28, 2014; Editors N. S. Mankoc Borstnik, H. B. Nielsen and D. Lukman; ISSN 1580-4992; book series: Bled Workshops in Physics vol. 15, no. 2, pp. 115-122 (2014