Second order semiclassics with self-generated magnetic fields

We consider the semiclassical asymptotics of the sum of negative eigenvalues of the three-dimensional Pauli operator with an external potential and a self-generated magnetic field $B$. We also add the field energy $\beta \int B^2$ and we minimize over all magnetic fields. The parameter $\beta$ effectively determines the strength of the field. We consider the weak field regime with $\beta h^{2}\ge {const}>0$, where $h$ is the semiclassical parameter. For smooth potentials we prove that the semiclassical asymptotics of the total energy is given by the non-magnetic Weyl term to leading order with an error bound that is smaller by a factor h^{1+\e}, i.e. the subleading term vanishes. However, for potentials with a Coulomb singularity the subleading term does not vanish due to the non-semiclassical effect of the singularity. Combined with a multiscale technique, this refined estimate is used in the companion paper \cite{EFS3} to prove the second order Scott correction to the ground state energy of large atoms and molecules.Comment: Small typos corrected on Sep 24, 201

Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Goedel-like metrics, show that the Penrose limit of the M-theory Goedel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves.Comment: 20 pages, LaTeX2

Scott correction for large atoms and molecules in a self-generated magnetic field

We consider a large neutral molecule with total nuclear charge $Z$ in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Z\al^2\le \kappa_0 for a sufficiently small $\kappa_0$, where \al denotes the fine structure constant. We show that, in the simultaneous limit $Z\to\infty$, \al\to 0 such that \kappa =Z\al^2 is fixed, the ground state energy of the system is given by a two term expansion $c_1Z^{7/3} + c_2(\kappa) Z^2 + o(Z^2)$. The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion

No evidence that polymorphisms of brain regulator genes Microcephalin and ASPM are associated with general mental ability, head circumference or altruism

We test the hypothesis that polymorphisms of the brain regulator genes MCPH1 and ASPM contribute to variations in human brain size and its correlates. We measured general mental ability, head circumference and social intelligence in 644 Canadian adults (496 Caucasians, 36 Orientals, 84 Mixed Race/Other and 28 Blacks; 257 men and 387 women). The gene polymorphisms were assessed from buccal DNA; mental ability by Wonderlic Personnel Test and Multidimensional Aptitude Battery; head circumference by stretchless tape; and social intelligence by prosocial attitude questionnaires. Although all measures were construct valid and the allele frequencies showed expected population differences, no relationship was found between the genes and any of the criteria. Among Caucasian 18–25 year olds, for example, the two mental ability tests correlated with each other (r=0.78, N=476, p<0.001), with head circumference (r=0.17, N=182, p<0.05) and with prosocial attitudes (r=0.23, N=182, p<0.001)

Chemical telemetry of OH observed to measure interstellar magnetic fields

We present models for the chemistry in gas moving towards the ionization front of an HII region. When it is far from the ionization front, the gas is highly depleted of elements more massive than helium. However, as it approaches the ionization front, ices are destroyed and species formed on the grain surfaces are injected into the gas phase. Photodissociation removes gas phase molecular species as the gas flows towards the ionization front. We identify models for which the OH column densities are comparable to those measured in observations undertaken to study the magnetic fields in star forming regions and give results for the column densities of other species that should be abundant if the observed OH arises through a combination of the liberation of H2O from surfaces and photodissociation. They include CH3OH, H2CO, and H2S. Observations of these other species may help establish the nature of the OH spatial distribution in the clouds, which is important for the interpretation of the magnetic field results.Comment: 11 pages, 2 figures, accepted by Astrophysics and Space Scienc

The excitation spectrum for weakly interacting bosons in a trap

We investigate the low-energy excitation spectrum of a Bose gas confined in a trap, with weak long-range repulsive interactions. In particular, we prove that the spectrum can be described in terms of the eigenvalues of an effective one-particle operator, as predicted by the Bogoliubov approximation.Comment: LaTeX, 32 page

Homogeneity and plane-wave limits

We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the behaviour of (reductive) homogeneous structures under the plane-wave limit.Comment: In memory of Stanley Hobert, 33 pages. Minor corrections and some simplification of Section 4.3.

The most creative organization in the world? The BBC, 'creativity' and managerial style

The managerial styles of two BBC directors-general, John Birt and Greg Dyke, have often been contrasted but not so far analysed from the perspective of their different views of 'creative management'. This article first addresses the orthodox reading of 'Birtism'; second, it locates Dyke's 'creative' turn in the wider context of fashionable neo-management theory and UK government creative industries policy; third, it details Dyke's drive to change the BBC's culture; and finally, it concludes with some reflections on the uncertainties inherent in managing a creative organisation

Gravitational anomalies signaling the breakdown of classical gravity

Recent observations for three types of astrophysical systems severely challenge the GR plus dark matter scenario, showing a phenomenology which is what modified gravity theories predict. Stellar kinematics in the outskirts of globular clusters show the appearance of MOND type dynamics on crossing the $a_{0}$ threshold. Analysis shows a ``Tully-Fisher'' relation in these systems, a scaling of dispersion velocities with the fourth root of their masses. Secondly, an anomaly has been found at the unexpected scales of wide binaries in the solar neighbourhood. Binary orbital velocities cease to fall along Keplerian expectations, and settle at a constant value, exactly on crossing the $a_{0}$ threshold. Finally, the inferred infall velocity of the bullet cluster is inconsistent with the standard cosmological scenario, where much smaller limit encounter velocities appear. This stems from the escape velocity limit present in standard gravity; the ``bullet'' should not hit the ``target'' at more than the escape velocity of the joint system, as it very clearly did. These results are consistent with extended gravity, but would require rather contrived explanations under GR, each. Thus, observations now put us in a situation where modifications to gravity at low acceleration scales cease to be a matter of choice, to now become inevitable.Comment: 10 pages, 5 figures, Astrophysics and Space Science Proceedings 38, 4