Static Hopfions in the extended Skyrme-Faddeev model

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is an extension of the Skyrme-Faddeev model by the addition of a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled non-linear partial differential equations in two variables by a successive over-relaxation (SOR) method. We construct numerical solutions with Hopf charge up to four, and calculate their analytical behavior in some limiting cases. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms. Their energies and sizes tend to zero as that combination approaches a particular special value. We calculate the equivalent of the Vakulenko and Kapitanskii energy bound for the theory and find that it vanishes at that same special value of the coupling constants. In addition, the model presents an integrable sector with an infinite number of local conserved currents which apparently are not related to symmetries of the action. In the intersection of those two special sectors the theory possesses exact vortex solutions (static and time dependent) which were constructed in a previous paper by one of the authors. It is believed that such model describes some aspects of the low energy limit of the pure SU(2) Yang-Mills theory, and our results may be important in identifying important structures in that strong coupling regime.Comment: 22 pages, 42 figures, minor correction

On the Strong Coupling Limit of the Faddeev-Hopf Model

The variational calculus for the Faddeev-Hopf model on a general Riemannian domain, with general Kaehler target space, is studied in the strong coupling limit. In this limit, the model has key similarities with pure Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group. The first and second variation formulae are calculated and several examples of stable solutions are obtained. In particular, it is proved that all immersive solutions are stable. Topological lower energy bounds are found in dimensions 2 and 4. An explicit description of the spectral behaviour of the Hopf map S^3 -> S^2 is given, and a conjecture of Ward concerning the stability of this map in the full Faddeev-Hopf model is proved.Comment: 21 pages, 0 figure

Gauge Dependence of Mass and Condensate in Chirally Asymmetric Phase of Quenched QED3

We study three dimensional quenched Quantum Electrodynamics in the bare vertex approximation. We investigate the gauge dependence of the dynamically generated Euclidean mass of the fermion and the chiral condensate for a wide range of values of the covariant gauge parameter $\xi$. We find that (i) away from $\xi=0$, gauge dependence of the said quantities is considerably reduced without resorting to sophisticated vertex {\em ansatze}, (ii) wavefunction renormalization plays an important role in restoring gauge invariance and (iii) the Ward-Green-Takahashi identity seems to increase the gauge dependence when used in conjunction with some simplifying assumptions. In the Landau gauge, we also verify that our results are in agreement with those based upon dimensional regularization scheme within the numerical accuracy available.Comment: 14 pages, 11 figures, uses revte

Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics

We study the gauge covariance of the massive fermion propagator in three as well as four dimensional Quantum Electrodynamics (QED). Starting from its value at the lowest order in perturbation theory, we evaluate a non-perturbative expression for it by means of its Landau-Khalatnikov-Fradkin (LKF) transformation. We compare the perturbative expansion of our findings with the known one loop results and observe perfect agreement upto a gauge parameter independent term, a difference permitted by the structure of the LKF transformations.Comment: 9 pages, no figures, uses revte

Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies

We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the configuration of N-soliton solution has N isolated localized energy densities and the each solitary wave-packet preserves its shape and velocity in the scattering process. The phase shifts are also the same as commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE

The impact of HIV infection on skeletal maturity in peripubertal children in Zimbabwe: a cross-sectional study

Introduction HIV infection and its treatment compromises skeletal development (growth and maturation). Skeletal maturity is assessed as bone age (BA) on hand and wrist radiographs. BA younger than chronological age (CA) indicates delayed development. We conducted a cross-sectional study to determine differences between BA and CA (i.e., skeletal maturity deviation [SMD]), and risk factors associated with SMD in peripubertal children with and without HIV established on antiretroviral therapy (ART) including use of tenofovir disoproxil fumarate (TDF). Methods Children with HIV taking ART for at least two years and a comparison group of HIV-negative children, aged 8–16 years and frequency-matched by age and sex, were recruited from HIV clinics and local schools in the same catchment area, in Harare, Zimbabwe. BA was assessed from non-dominant hand-wrist radiographs using the Tanner Whitehouse 3 method. Negative SMD values correspond to delayed development, i.e., BA younger than CA. Multivariable linear regression models determined factors associated with SMD overall, and in children with HIV. Results In total, 534 participants (54% males) were included; by design CA was similar in males and females, whether living with or without HIV. Mean (SD) SMD was more negative in CWH than in HIV-negative children in both males [-1.4(1.4) vs. -0.4(1.1) years] and females [-1.1(1.3) vs. -0.0(1.2) years]. HIV infection and weight-for-age Z-score<-2 were associated with more negative SMD in both males and females after adjusting for socio-economic status, orphanhood, pubertal stage, and calcium intake. Age at ART initiation was associated with SMD in both males and females with those starting ART later more delayed: starting ART aged 4–8 years 1.14 (-1.84, -0.43), or over 8 years 1.47 (-2.30, -0.65) (p-value for trend < 0.001). Similar non-significant trends were seen in males. TDF exposure TDF exposure whether < 4years or ≥ 4 years was not associated with delayed development. Conclusion Perinatally-acquired HIV infection and being underweight were independently associated with delayed skeletal maturation in both males and females. Starting ART later was independently associated with skeletal maturation delay in CWH. Given the known effects of delayed development on later health, it is important to find interventions to ensure healthy weight gain through early years and in CWH to initiate ART as early as possible

Simulation of dimensionality effects in thermal transport

The discovery of nanostructures and the development of growth and fabrication techniques of one- and two-dimensional materials provide the possibility to probe experimentally heat transport in low-dimensional systems. Nevertheless measuring the thermal conductivity of these systems is extremely challenging and subject to large uncertainties, thus hindering the chance for a direct comparison between experiments and statistical physics models. Atomistic simulations of realistic nanostructures provide the ideal bridge between abstract models and experiments. After briefly introducing the state of the art of heat transport measurement in nanostructures, and numerical techniques to simulate realistic systems at atomistic level, we review the contribution of lattice dynamics and molecular dynamics simulation to understanding nanoscale thermal transport in systems with reduced dimensionality. We focus on the effect of dimensionality in determining the phononic properties of carbon and semiconducting nanostructures, specifically considering the cases of carbon nanotubes, graphene and of silicon nanowires and ultra-thin membranes, underlying analogies and differences with abstract lattice models.Comment: 30 pages, 21 figures. Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Renormalization and Chiral Symmetry Breaking in Quenched QED in Arbitrary Covariant Gauge

We extend a previous Landau-gauge study of subtractive renormalization of the fermion propagator Dyson-Schwinger equation (DSE) in strong-coupling, quenched QED_4 to arbitrary covariant gauges. We use the fermion-photon proper vertex proposed by Curtis and Pennington with an additional correction term included to compensate for the small gauge-dependence induced by the ultraviolet regulator. We discuss the chiral limit and the onset of dynamical chiral symmetry breaking in the presence of nonperturbative renormalization. We extract the critical coupling in several different gauges and find evidence of a small residual gauge-dependence in this quantity.Comment: REVTEX 3.0, 27 pages including 14 Extended Postscript files comprising 9 figures. Replacement: discussion of chiral limit corrected, and some minor typographical errors fixed. To appear in Phys. Rev.