A Lorentz-invariant look at quantum clock synchronization protocols based on distributed entanglement

Recent work has raised the possibility that quantum information theory techniques can be used to synchronize atomic clocks nonlocally. One of the proposed algorithms for quantum clock synchronization (QCS) requires distribution of entangled pure singlets to the synchronizing parties. Such remote entanglement distribution normally creates a relative phase error in the distributed singlet state which then needs to be purified asynchronously. We present a fully relativistic analysis of the QCS protocol which shows that asynchronous entanglement purification is not possible, and, therefore, that the proposed QCS scheme remains incomplete. We discuss possible directions of research in quantum information theory which may lead to a complete, working QCS protocol.Comment: 5 pages; typeset in RevTe

Singularities in the Kerr-Newman and charged δ=2\delta=2 Tomimatsu-Sato spacetimes endowed with negative mass

The Kerr-Newman solution with negative mass is shown to develop a massless ring singularity off the symmetry axis. The singularity is located inside the region with closed timelike curves which has topology of a torus and lies outside the ergoregion. These characteristics are also shared by the charged Tomimatsu-Sato delta=2 solution with negative total mass to which in particular a simple form in terms of four polynomials is provided.Comment: 10 pages, 7 figures; hyperextreme case included, one reference adde

Cross section of the processes e++e−→e++e−(γ)e^++e^-\to e^++e^-(\gamma), →π++π−(γ)\to \pi^++\pi^-(\gamma), μ++μ−(γ) \mu^++\mu^-(\gamma), γ+γ(γ) \gamma+\gamma(\gamma) in the energy region 200 MeV ≤2E≤\le 2E\le 3 GeV

The cross section for different processes induced by $e^+e^-$ annihilation, in the kinematical limit $\beta_{\mu}\approx\beta_{\pi}=(1-m_{\pi}^2/\epsilon^2)^{1/2}\sim 1$, is calculated taking into account first order corrections to the amplitudes and the corrections due to soft emitted photons, with energy $\omega\le\Delta E\le \epsilon$ in the center of mass of the $e^+e^-$ colliding beams. The results are given separately for charge--odd and charge--even terms in the final channels $\pi^+\pi^-(\gamma)$ and $\mu^+\mu^-(\gamma)$. In case of pions, form factors are taken into account. The differential cross sections for the processes: $e^++e^-\to e^++e^-(+\gamma)$, $\to \pi^++\pi^-(\gamma)$, $\to \mu^++\mu^-(\gamma),\to \gamma\gamma(\gamma)$ have been calculated and the corresponding formula are given in the ultrarelativistic limit $\sqrt{s}/2= \epsilon \gg m_{\mu}\sim m_{\pi}$ . For a quantitative evaluation of the contribution of higher order of the perturbation theory, the production of $\pi^+\pi^-$, including radiative corrections, is calculated in the approach of the lepton structure functions. This allows to estimate the precision of the obtained results as better than 0.5% outside the energy region corresponding to narrow resonances. A method to integrate the cross section, avoiding the difficulties which arise from singularities is also described.Comment: 25 pages 3 firgur

Closure properties of solutions to heat inequalities

We prove that if $u_1,u_2 : (0,\infty) \times \R^d \to (0,\infty)$ are sufficiently well-behaved solutions to certain heat inequalities on $\R^d$ then the function $u: (0,\infty) \times \R^d \to (0,\infty)$ given by $u^{1/p}=u_1^{1/p_1} * u_2^{1/p_2}$ also satisfies a heat inequality of a similar type provided $\tfrac{1}{p_1} + \tfrac{1}{p_2} = 1 + \tfrac{1}{p}$. On iterating, this result leads to an analogous statement concerning $n$-fold convolutions. As a corollary, we give a direct heat-flow proof of the sharp $n$-fold Young convolution inequality and its reverse form.Comment: 12 page

Early Mississippian sandy siltstones preserve rare vertebrate fossils in seasonal flooding episodes

Flood-generated sandy siltstones are under-recognised deposits that preserve key vertebrate (actinopterygians, rhizodonts, and rarer lungfish, chondrichthyans and tetrapods), invertebrate and plant fossils. Recorded for the first time from the lower Mississippian Ballagan Formation of Scotland, more than 140 beds occur throughout a 490 m thick core succession charac-terised by fluvial sandstones, palaeosols, siltstones, dolostone ‘cementstones’ and gypsum from a coastal–alluvial plain setting. Sandy siltstones are described as a unique taphofacies of the Ballagan Formation (Scotland, UK);they are matrix-supported siltstones with millimetre-sized siltstone and very fine sandstone lithic clasts. Common bioclasts include plants and mega-spores, fish, ostracods, eurypterids and bivalves. Fossils have a high degree of articulation compared with those found in other fossil-bearing deposits, such as conglomerate lags at the base of fluvial channel sandstones. Bed thickness and distribution varies throughout the formation, with no stratigraphic trend. The matrix sediment and clasts are sourced from the reworking of floodplain sediments including desiccated surfaces and palaeosols. Secondary pedogenic modification affects 30% of the sandy siltstone beds and most (71%) overlie palaeosols or desiccation cracks. Sandy siltstones are interpreted as cohesive debris flow deposits that originated by the over-bank flooding of rivers and due to localised floodplain sediment transport at times of high rainfall; their association with palaeosols and desiccation cracks indicates seasonally wet to dry cycles throughout the Tournaisian. Tetrapod and fish fossils derived from floodplain lakes and land surfaces are concentrated by local erosion and reworking, and are preserved by deposition into temporary lakes on the floodplain; their distribution indicates a local origin, with sediment transported across the floodplain in seasonal rainfall episodes. These deposits are significant new sites that can be explored for the preservation of rare non-marine fossil material and provide unique insights into the evolution of early terrestrial ecosystems

Entanglement of two-mode Bose-Einstein condensates

We investigate the entaglement characteristics of two general bimodal Bose-Einstein condensates - a pair of tunnel-coupled Bose-Einstein condensates and the atom-molecule Bose-Einstein condensate. We argue that the entanglement is only physically meaningful if the system is viewed as a bipartite system, where the subsystems are the two modes. The indistinguishibility of the particles in the condensate means that the atomic constituents are physically inaccessible and thus the degree of entanglement between individual particles, unlike the entanglement between the modes, is not experimentally relevant so long as the particles remain in the condensed state. We calculate the entanglement between the modes for the exact ground state of the two bimodal condensates and consider the dynamics of the entanglement in the tunnel-coupled case.Comment: 11 pages, 8 figures, submitted to Physical Review A, to be presented at the third UQ Mathematical Physics workshop, Oct. 4-6; changes made in response to referee comment

The mediating effect of task presentation on collaboration and children's acquisition of scientific reasoning

There has been considerable research concerning peer interaction and the acquisition of children's scientific reasoning. This study investigated differences in collaborative activity between pairs of children working around a computer with pairs of children working with physical apparatus and related any differences to the development of children's scientific reasoning. Children aged between 9 and 10 years old (48 boys and 48 girls) were placed into either same ability or mixed ability pairs according to their individual, pre-test performance on a scientific reasoning task. These pairs then worked on either a computer version or a physical version of Inhelder and Piaget's (1958) chemical combination task. Type of presentation was found to mediate the nature and type of collaborative activity. The mixed-ability pairs working around the computer talked proportionally more about the task and management of the task; had proportionally more transactive discussions and used the record more productively than children working with the physical apparatus. Type of presentation was also found to mediated children's learning. Children in same ability pairs who worked with the physical apparatus improved significantly more than same ability pairs who worked around the computer. These findings were partially predicted from a socio-cultural theory and show the importance of tools for mediating collaborative activity and collaborative learning

Reinterpreting the age of the uppermost ‘Old Red Sandstone’ and Early Carboniferous in Scotland

In Scotland, the base of the Ballagan Formation has traditionally been placed at the first grey mudstone within a contiguous Late Devonian to Carboniferous succession. This convention places the Devonian–Carboniferous boundary within the Old Red Sandstone (ORS) Kinnesswood Formation. The consequences of this placement are that tetrapods from the Ballagan Formation were dated as late Tournaisian in age and that the ranges of typically Devonian fish found in the Kinnesswood Formation continued into the Carboniferous. The Pease Bay specimen of the fish Remigolepis is from the Kinnesswood Formation. Comparisons with its range in Greenland, calibrated against spores, show it was Famennian in age. Detailed palynological sampling at Burnmouth from the base of the Ballagan Formation proves that the early Tournaisian spore zones (VI and HD plus Cl 1) are present. The Schopfites species that occurs through most of the succession is Schopfites delicatus rather than Schopfites claviger. The latter species defines the late Tournaisian CM spore zone. The first spore assemblage that has been found in Upper ‘ORS' strata underlying the Ballagan Formation (Preston, Whiteadder Water), contains Retispora lepidophyta and is from the early latest Famennian LL spore zone. The spore samples are interbedded with volcaniclastic debris, which shows that the Kelso Volcanic Formation is, in part, early latest Famennian in age. These findings demonstrate that the Ballagan Formation includes most of the Tournaisian with the Devonian–Carboniferous boundary positioned close to the top of the Kinnesswood Formation. The Stage 6 calcrete at Pease Bay can be correlated to the equivalent section at Carham, showing that it represents a time gap equivalent to the latest Famennian glaciation(s). Importantly, some of the recently described Ballagan Formation tetrapods are older than previously dated and now fill the key early part of Romer's Gap

The terrestrial landscapes of tetrapod evolution in earliest Carboniferous seasonal wetlands of SE Scotland

The Lower Mississippian (Tournaisian) Ballagan Formation in SE Scotland yields tetrapod fossils that provide fresh insights into the critical period when these animals first moved onto land. The key to understanding the palaeoenvironments where they lived is a detailed analysis of the sedimentary architecture of this formation, one of the thickest and most completely documented examples of a coastal floodplain and marginal marine succession from this important transitional time anywhere in the world. Palaeosols are abundant, providing a unique insight into the early Carboniferous habitats and climate. More than 200 separate palaeosols are described from three sections through the formation. The palaeosols range in thickness from 0.02 to 1.85 m and are diverse: most are Entisols and Inceptisols (63%), indicating relatively brief periods of soil development. Gleyed Inseptisols and Vertisols are less common (37%). Vertisols are the thickest palaeosols (up to 185 cm) in the Ballagan Formation and have common vertic cracks. Roots are abundant through all the palaeosols, from shallow mats and thin hair-like traces to sporadic thicker root traces typical of arborescent lycopods. Geochemical, isotope and clay mineralogical analyses of the palaeosols indicate a range in soil alkalinity and amount of water logging. Estimates of mean annual rainfall from palaeosol compositions are 1000 –1500 mm per year. The high mean annual rainfall and variable soil alkalinities contrast markedly with dry periods that developed deep penetrating cracks and evaporite deposits. It is concluded that during the early Carboniferous, this region experienced a sharply contrasting seasonal climate and that the floodplain hosted a mosaic of closely juxtaposed but distinct habitats in which the tetrapods lived. The diversification of coastal floodplain environments identified here may link to the evolution and movement of tetrapods into the terrestrial realm

Parity nonconservation in heavy atoms: The radiative correction enhanced by the strong electric field of the nucleus

Parity nonconservation due to the nuclear weak charge is considered. We demonstrate that the radiative corrections to this effect due to the vacuum fluctuations of the characteristic size larger than the nuclear radius $r_0$ and smaller than the electron Compton wave-length $\lambda_C$ are enhanced because of the strong electric field of the nucleus. The parameter that allows one to classify the corrections is the large logarithm $\ln(\lambda_C/r_0)$. The vacuum polarization contribution is enhanced by the second power of the logarithm. Although the self-energy and the vertex corrections do not vanish, they contain only the first power of the logarithm. The value of the radiative correction is 0.4% for Cs and 0.9% for Tl, Pb, and Bi. We discuss also how the correction affects the interpretation of the experimental data on parity nonconservation in atoms.Comment: 4 pages, 3 figures, RevTe