Linked and knotted beams of light, conservation of helicity and the flow of null electromagnetic fields

Maxwell's equations allow for some remarkable solutions consisting of pulsed beams of light which have linked and knotted field lines. The preservation of the topological structure of the field lines in these solutions has previously been ascribed to the fact that the electric and magnetic helicity, a measure of the degree of linking and knotting between field lines, are conserved. Here we show that the elegant evolution of the field is due to the stricter condition that the electric and magnetic fields be everywhere orthogonal. The field lines then satisfy a `frozen field' condition and evolve as if they were unbreakable filaments embedded in a fluid. The preservation of the orthogonality of the electric and magnetic field lines is guaranteed for null, shear-free fields such as the ones considered here by a theorem of Robinson. We calculate the flow field of a particular solution and find it to have the form of a Hopf fibration moving at the speed of light in a direction opposite to the propagation of the pulsed light beam, a familiar structure in this type of solution. The difference between smooth evolution of individual field lines and conservation of electric and magnetic helicity is illustrated by considering a further example in which the helicities are conserved, but the field lines are not everywhere orthogonal. The field line configuration at time t=0 corresponds to a nested family of torus knots but unravels upon evolution

Realisation of Hardy's Thought Experiment

We present an experimental realisation of Hardy's thought experiment [Phys. Rev. Lett. {\bf 68}, 2981 (1992)], using photons. The experiment consists of a pair of Mach-Zehnder interferometers that interact through photon bunching at a beam splitter. A striking contradiction is created between the predictions of quantum mechanics and local hidden variable based theories. The contradiction relies on non-maximally entangled position states of two particles.Comment: 5 page

Effects of restricted basilar papillar lesions and hair cell regeneration on auditory forebrain frequency organization in adult European Starlings

The frequency organization of neurons in the forebrain Field L complex (FLC) of adult starlings was investigated to determine the effects of hair cell (HC) destruction in the basal portion of the basilar papilla (BP) and of subsequent HC regeneration. Conventional microelectrode mapping techniques were used in normal starlings and in lesioned starlings either 2 d or 6-10 weeks after aminoglycoside treatment. Histological examination of the BP and recordings of auditory brainstem evoked responses confirmed massive loss of HCs in the basal portion of the BP and hearing losses at frequencies >2 kHz in starlings tested 2 d after aminoglycoside treatment. In these birds, all neurons in the region of the FLC in which characteristic frequencies (CFs) normally increase from 2 to 6 kHz had CF in the range of 2-4 kHz. The significantly elevated thresholds of responses in this region of altered tonotopic organization indicated that they were the residue of prelesion responses and did not reflect CNS plasticity. In the long-term recovery birds, there was histological evidence of substantial HC regeneration. The tonotopic organization of the high-frequency region of the FLC did not differ from that in normal starlings, but the mean threshold at CF in this frequency range was intermediate between the values in the normal and lesioned short-recovery groups. The recovery of normal tonotopicity indicates considerable stability of the topography of neuronal connections in the avian auditory system, but the residual loss of sensitivity suggests deficiencies in high-frequency HC function

Integral-Field Spectroscopy of the Post Red Supergiant IRC +10420: evidence for an axi-symmetric wind

We present NAOMI/OASIS adaptive-optics assisted integral-field spectroscopy of the transitional massive hypergiant IRC +10420, an extreme mass-losing star apparently in the process of evolving from a Red Supergiant toward the Wolf-Rayet phase. To investigate the present-day mass-loss geometry of the star, we study the appearance of the line-emission from the inner wind as viewed when reflected off the surrounding nebula. We find that, contrary to previous work, there is strong evidence for wind axi-symmetry, based on the equivalent-width and velocity variations of H$\alpha$ and Fe {\sc ii} $\lambda$6516. We attribute this behaviour to the appearance of the complex line-profiles when viewed from different angles. We also speculate that the Ti {\sc ii} emission originates in the outer nebula in a region analogous to the Strontium Filament of $\eta$ Carinae, based on the morphology of the line-emission. Finally, we suggest that the present-day axisymmetric wind of IRC +10420, combined with its continued blueward evolution, is evidence that the star is evolving toward the B[e] supergiant phase.Comment: 22 pages, 9 figures, accepted for publication in ApJ. B&W-optimized version can be downloaded from http://www.cis.rit.edu/~bxdpci/pubs.htm

Reconfigurable Boolean Logic using Magnetic Single-Electron Transistors

We propose a novel hybrid single-electron device for reprogrammable low-power logic operations, the magnetic single-electron transistor (MSET). The device consists of an aluminium single-electron transistors with a GaMnAs magnetic back-gate. Changing between different logic gate functions is realized by reorienting the magnetic moments of the magnetic layer which induce a voltage shift on the Coulomb blockade oscillations of the MSET. We show that we can arbitrarily reprogram the function of the device from an n-type SET for in-plane magnetization of the GaMnAs layer to p-type SET for out-of-plane magnetization orientation. Moreover, we demonstrate a set of reprogrammable Boolean gates and its logical complement at the single device level. Finally, we propose two sets of reconfigurable binary gates using combinations of two MSETs in a pull-down network

Mass Dependence of M3Y-Type Interactions and the Effects of Tensor Correlations

The mass dependence of the M3Y-type effective interactions and the effects of tensor correlations are examined. Two-body nuclear matrix elements are obtained by the lowest order constrained variational (LOCV) technique with and without tensor correlations. We have found that the tensor correlations are important especially in the triplet-even (TE) and tensor-even (TNE) channels in order to reproduce the G-matrix elements obtained previously. Then M3Y-type potentials for inelastic scattering are obtained by fitting our two-body matrix elements to those of a sum of Yukawa functions for the mass numbers A=24, A=40 and A=90.Comment: 13 pages, 6 table