Non-locality of Foldy-Wouthuysen and related transformations for the Dirac equation

Non-localities of Foldy-Wouthuysen and related transformations, which are used to separate positive and negative energy states in the Dirac equation, are investigated. Second moments of functional kernels generated by the transformations are calculated, the transformed functions and their variances are computed. It is shown that all the transformed quantities are smeared in the coordinate space by the amount comparable to the Compton wavelength $\lambda_c=\hbar/mc$.Comment: 7 pages, two figure

Zitterbewegung of relativistic electrons in a magnetic field and its simulation by trapped ions

One-electron 3+1 and 2+1 Dirac equations are used to calculate the motion of a relativistic electron in a vacuum in the presence of an external magnetic field. First, calculations are carried on an operator level and exact analytical results are obtained for the electron trajectories which contain both intraband frequency components, identified as the cyclotron motion, as well as interband frequency components, identified as the trembling motion (Zitterbewegung, ZB). Next, time-dependent Heisenberg operators are used for the same problem to compute average values of electron position and velocity employing Gaussian wave packets. It is shown that the presence of a magnetic field and the resulting quantization of the energy spectrum has pronounced effects on the electron Zitterbewegung: it introduces intraband frequency components into the motion, influences all the frequencies and makes the motion stationary (not decaying in time) in case of the 2+1 Dirac equation. Finally, simulations of the 2+1 Dirac equation and the resulting electron ZB in the presence of a magnetic field are proposed and described employing trapped ions and laser excitations. Using simulation parameters achieved in recent experiments of Gerritsma and coworkers we show that the effects of the simulated magnetic field on ZB are considerable and can certainly be observed.Comment: 19 pages, 9 figures, published versio

One-dimensional semirelativity for electrons in carbon nanotubes

It is shown that the band structure of single-wall semiconducting carbon nanotubes (CNT) is analogous to relativistic description of electrons in vacuum, with the maximum velocity $u$= $10^8$cm/s replacing the light velocity. One-dimensional semirelativistic kinematics and dynamics of electrons in CNT is formulated. Two-band k.p Hamiltonian is employed to demonstrate that electrons in CNT experience a Zitterbewegung (trembling motion) in absence of external fields. This Zitterbewegung should be observable much more easily in CNT than its analogue for free relativistic electrons in vacuum.Comment: 4 pages no figure

Transient Zitterbewegung of charge carriers in graphene and carbon nanotubes

Observable effects due to trembling motion (Zitterbewegung, ZB) of charge carriers in bilayer graphene, monolayer graphene and carbon nanotubes are calculated. It is shown that, when the charge carriers are prepared in the form of gaussian wave packets, the ZB has a transient character with the decay time of femtoseconds in graphene and picoseconds in nanotubes. Analytical results for bilayer graphene allow us to investigate phenomena which accompany the trembling motion. In particular, it is shown that the transient character of ZB in graphene is due to the fact that wave subpackets related to positive and negative electron energies move in opposite directions, so their overlap diminishes with time. This behavior is analogous to that of the wave packets representing relativistic electrons in a vacuum.Comment: 7 pages, 3 figures, augmented versio

Epicyclic orbital oscillations in Newton's and Einstein's dynamics

We apply Feynman's principle, ``The same equations have the same solutions'', to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical geometry of Schwarzschild's spacetime. For this reason, rather unexpectedly, Newton's formulae for Kepler's problem, in the case of nearly circular motion in a static, spherically spherical gravitational potential accurately describe strong field general relativistic effects, in particular vanishing of the radial epicyclic frequency at the marginally stable orbit.Comment: 8 page

Stage of perinatal development regulates skeletal muscle mitochondrial biogenesis and myogenic regulatory factor genes with little impact of growth restriction or cross-fostering

Foetal growth restriction impairs skeletal muscle development and adult muscle mitochondrial biogenesis. We hypothesized that key genes involved in muscle development and mitochondrial biogenesis would be altered following uteroplacental insufficiency in rat pups, and improving postnatal nutrition by cross-fostering would ameliorate these deficits. Bilateral uterine vessel ligation (Restricted) or sham (Control) surgery was performed on day 18 of gestation. Males and females were investigated at day 20 of gestation (E20), 1 (PN1), 7 (PN7) and 35 (PN35) days postnatally. A separate cohort of Control and Restricted pups were cross-fostered onto a different Control or Restricted mother and examined at PN7. In both sexes, peroxisome proliferator-activated receptor (PPAR)-&gamma; coactivator-1&alpha; (PGC-1&alpha;), cytochrome c oxidase subunits 3 and 4 (COX III and IV) and myogenic regulatory factor 4 expression increased from late gestation to postnatal life, whereas mitochondrial transcription factor A, myogenic differentiation 1 (MyoD), myogenin and insulin-like growth factor I (IGF-I) decreased. Foetal growth restriction increased MyoD mRNA in females at PN7, whereas in males IGF-I mRNA was higher at E20 and PN1. Cross-fostering Restricted pups onto a Control mother significantly increased COX III mRNA in males and COX IV mRNA in both sexes above controls with little effect on other genes. Developmental age appears to be a major factor regulating skeletal muscle mitochondrial and developmental genes, with growth restriction and cross-fostering having only subtle effects. It therefore appears that reductions in adult mitochondrial biogenesis markers likely develop after weaning.<br /

Zitterbewegung of Klein-Gordon particles and its simulation by classical systems

The Klein-Gordon equation is used to calculate the Zitterbewegung (ZB, trembling motion) of spin-zero particles in absence of fields and in the presence of an external magnetic field. Both Hamiltonian and wave formalisms are employed to describe ZB and their results are compared. It is demonstrated that, if one uses wave packets to represent particles, the ZB motion has a decaying behavior. It is also shown that the trembling motion is caused by an interference of two sub-packets composed of positive and negative energy states which propagate with different velocities. In the presence of a magnetic field the quantization of energy spectrum results in many interband frequencies contributing to ZB oscillations and the motion follows a collapse-revival pattern. In the limit of non-relativistic velocities the interband ZB components vanish and the motion is reduced to cyclotron oscillations. The exact dynamics of a charged Klein-Gordon particle in the presence of a magnetic field is described on an operator level. The trembling motion of a KG particle in absence of fields is simulated using a classical model proposed by Morse and Feshbach -- it is shown that a variance of a Gaussian wave packet exhibits ZB oscillations.Comment: 16 pages and 7 figure

Maternal obesity in females born small: pregnancy complications and offspring disease risk

Obesity is a major public health crisis, with 1.6 billion adults worldwide being classified as overweight or obese in 2014. Therefore, it is not surprising that the number of women who are overweight or obese at the time of conception is increasing. Obesity during pregnancy is associated with the development of gestational diabetes and preeclampsia. The developmental origins of health and disease hypothesis proposes that perturbations during critical stages of development can result in adverse fetal changes, which leads to an increased risk of developing diseases in adulthood. Of particular concern, children born to obese mothers are at a greater risk of developing cardiometabolic disease. One subset of the population who are predisposed to developing obesity are children born small for gestational age, which occurs in 10% of pregnancies worldwide. Epidemiological studies report that these growth restricted children have an increased susceptibility to type 2 diabetes, obesity and hypertension. Importantly during pregnancy, growth restricted females have a higher risk of developing cardiometabolic disease, indicating that they may have an exacerbated phenotype if they are also overweight or obese. Thus the development of early pregnancy interventions targeted to obese mothers may prevent their children from developing cardiometabolic disease in adulthood. This article is protected by copyright. All rights reserved

Non-locality of energy separating transformations for Dirac electrons in a magnetic field

We investigate a non-locality of Moss-Okninski transformation (MOT) used to separate positive and negative energy states in the 3+1 Dirac equation for relativistic electrons in the presence of a magnetic field. Properties of functional kernels generated by the MOT are analyzed and kernel non-localities are characterized by calculating their second moments parallel and perpendicular to the magnetic field. Transformed functions are described and investigated by computing their variances. It is shown that the non-locality of the energy-separating transformation in the direction parallel to the magnetic field is characterized by the Compton wavelength $\lambda_c=\hbar/mc$. In the plane transverse to magnetic field the non-locality depends both on magnetic radius $L=(\hbar/eB)^{1/2}$ and $\lambda_c$. The non-locality of MO transformation for the 2+1 Dirac equation is also considered.Comment: 11 pages 3 figure

Genomic analysis of Campylobacter fetus subspecies: identification of candidate virulence determinants and diagnostic assay targets

Background: Campylobacter fetus subspecies venerealis is the causative agent of bovine genital campylobacteriosis, asymptomatic in bulls the disease is spread to female cattle causing extensive reproductive loss. The microbiological and molecular differentiation of C. fetus subsp. venerealis from C. fetus subsp. fetus is extremely difficult. This study describes the analysis of the available C. fetus subsp. venerealis AZUL-94 strain genome (~75–80%) to identify elements exclusively found in C. fetus subsp. venerealis strains as potential diagnostic targets and the characterisation of subspecies virulence genes. Results: Eighty Kb of genomic sequence (22 contigs) was identified as unique to C. fetus subsp. venerealis AZUL-94 and consisted of type IV secretory pathway components, putative plasmid genes and hypothetical proteins. Of the 9 PCR assays developed to target C. fetus subsp. venerealis type IV secretion system genes, 4 of these were specific for C. fetus subsp. venerealis biovar venerealis and did not detect C. fetus subsp. venerealis biovar intermedius. Two assays were specific for C. fetus subsp. venerealis AZUL-94 strain, with a further single assay specific for the AZUL-94 strain and C. fetus subsp. venerealis biovar intermedius (and not the remaining C. fetus subsp. venerealis biovar venerealis strains tested). C. fetus subsp. fetus and C. fetus subsp. venerealis were found to share most common Campylobacter virulence factors such as SAP, chemotaxis, flagellar biosynthesis, 2-component systems and cytolethal distending toxin subunits (A, B, C). We did not however, identify in C. fetus the full complement of bacterial adherence candidates commonly found in other Campylobacter spp. Conclusion: The comparison of the available C. fetus subsp. venerealis genome sequence with the C. fetus subsp. fetus genome identified 80 kb of unique C. fetus subsp. venerealis AZUL94 sequence, with subsequent PCR confirmation demonstrating inconsistent amplification of these targets in all other C. fetus subsp. venerealis strains and biovars tested. The assays developed here highlight the complexity of targeting strain specific virulence genes for field studies for the molecular identification and epidemiology of C. fetus