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

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

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 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

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

Atomic Scale Structure and Chemical Composition across Order-Disorder Interfaces

Through a combination of aberration-corrected high-resolution scanning transmission electron microscopy and three-dimensional atom probe tomography, the true atomic-scale structure and change in chemical composition across the complex order-disorder interface in a metallic alloy has been determined. The study reveals the presence of two interfacial widths, one corresponding to an order-disorder transition, and the other to the compositional transition across the interface, raising fundamental questions regarding the definition of the interfacial width in such systems

Observation of Two Narrow States Decaying into Ξc+γ\Xi_{c}^{+}\gamma and Ξc0γ\Xi_{c}^{0}\gamma

We report the first observation of two narrow charmed strange baryons decaying to $\Xi_c^+\gamma$ and $\Xi_c^0\gamma$, respectively, using data from the CLEO II detector at CESR. We interpret the observed signals as the $\Xi_c^{+\prime}(c{su})$ and $\Xi_c^{0\prime}(c{sd})$, the symmetric partners of the well-established antisymmetric $\Xi_c^+(c[su])$ and $\Xi_c^0(c[sd])$. The mass differences $M(\Xi_c^{+\prime})-M(\Xi_c^+)$ and $M(\Xi_c^{0\prime})-M(\Xi_c^0)$ are measured to be $107.8\pm 1.7\pm 2.5$ and $107.0\pm 1.4\pm 2.5 MeV/c^2$, respectively.Comment: 11 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN