Spacetime Encodings II - Pictures of Integrability

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a two degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about two degree of freedom systems. Evidence is given, in the form of orbit-crossing structure, that geodesics in SAV spacetimes might admit, a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 figure

Orbital excitations in LaMnO3_3

We study the recently observed orbital excitations, orbitons, and treat electron-electron correlations and lattice dynamics on equal footing. It is shown that the orbiton energy and dispersion are determined by both correlations and lattice-vibrations. The electron-phonon coupling causes satellite structures in the orbiton spectral function and the elementary excitations of the system are mixed modes with both orbital and phonon character. It is proposed that the satellite structures observed in recent Raman-scattering experiments on LaMnO$_3$ are actually orbiton derived satellites in the phonon spectral function, caused by the phonon-orbiton interaction.Comment: 4 pages, 3 figures embedde

Analysis of Oct4-dependent transcriptional networks regulating self-renewal and pluripotency in human embryonic stem cells

The POU domain transcription factor OCT4 is a key regulator of pluripotency in the early mammalian embryo and is highly expressed in the inner cell mass of the blastocyst. Consistent with its essential role in maintaining pluripotency, Oct4 expression is rapidly downregulated during formation of the trophoblast lineage. To enhance our understanding of the molecular basis of this differentiation event in humans, we used a functional genomics approach involving RNA interference-mediated suppression of OCT4 function in a human ESC line and analysis of the resulting transcriptional profiles to identify OCT4-dependent genes in human cells. We detected altered expression of >1,000 genes, including targets regulated directly by OCT4 either positively (NANOG, SOX2, REX1, LEFTB, LEFTA/EBAF DPPA4, THY1, and TDGF1) or negatively (CDX2, EOMES, BMP4, TBX18, Brachyury [T], DKK1, HLX1, GATA6, ID2, and DLX5), as well as targets for the OCT4-associated stem cell regulators SOX2 and NANOG. Our data set includes regulators of ACTIVIN, BMP, fibroblast growth factor, and WNT signaling. These pathways are implicated in regulating human ESC differentiation and therefore further validate the results of our analysis. In addition, we identified a number of differentially expressed genes that are involved in epigenetics, chromatin remodeling, apoptosis, and metabolism that may point to underlying molecular mechanisms that regulate pluripotency and trophoblast differentiation in humans. Significant concordance between this data set and previous comparisons between inner cell mass and trophectoderm in human embryos indicates that the study of human ESC differentiation in vitro represents a useful model of early embryonic differentiation in humans

Excitonic quasiparticles in a spin-orbit Mott insulator

In condensed matter systems, out of a large number of interacting degrees of freedom emerge weakly coupled particles, in terms of which most physical properties are described. For example, Landau quasiparticles (QP) determine all electronic properties of a normal metal. The lack of identification of such QPs is major barrier for understanding myriad exotic properties of correlated electrons, such as unconventional superconductivity and non-Fermi liquid behaviours. Here, we report the observation of a composite particle in a Mott insulator Sr2IrO4---and exciton dressed with magnons---that propagates with the canonical characteristics of a QP: a finite QP residue and a lifetime longer than the hopping time scale. The dynamics of this charge-neutral bosonic excitation mirrors the fundamental process of the analogous one-hole propagation in the background of ordered spins, for which a well-defined QP has never been observed. The much narrower linewidth of the exciton reveals the same intrinsic dynamics that is obscured for the hole and is intimately related to the mechanism of high temperature superconductivity.Comment: submitted versio

G_2 invariant 7D Euclidean super Yang-Mills theory as a higher-dimensional analogue of the 3D super-BF theory

A formulation of the N_T=1, D=8 Euclidean super Yang-Mills theory with generalized self-duality and reduced Spin(7)-invariance is given which avoids the peculiar extra constraints of Nishino and Rajpoot, hep-th/0210132. Its reduction to 7 dimensions leads to the G_2-invariant N_T=2, D=7 super Yang-Mills theory which may be regarded as a higher-dimensional analogue of the N=2, D=3 super-BF theory. When reducing further that G_2-invariant theory to 3 dimensions one gets the N_T=2 super-BF theory coupled to a spinorial hypermultiplet.Comment: 9 pages, Late

Construction and analysis of a simplified many-body neutrino model

In dense neutrino systems, such as found in the early Universe, or near a supernova core, neutrino flavor evolution is affected by coherent neutrino-neutrino scattering. It has been recently suggested that many-particle quantum entanglement effects may play an essential role in these systems, potentially invalidating the traditional description in terms of a set of single-particle evolution equations. We model the neutrino system by a system of interacting spins, following an earlier work which showed that such a spin system can in some cases be solved exactly. We extend this work by constructing an exact analytical solution to a more general spin system, including initial states with asymmetric spin distribution and, moreover, not necessarily aligned along the same axis. Our solution exhibits a rich set of behaviors, including coherent oscillations and dephasing and a transition from the classical to quantum regimes. We argue that the classical evolution of the spin system captures the entire coherent behavior of the neutrino system, while the quantum effects in the spin system capture some, but not all, of the neutrino incoherent evolution. By comparing the spin and neutrino systems, we find no evidence for the violation of the accepted one-body description, though the argument involves some subtleties not appreciated before. The analysis in this paper may apply to other two-state systems beyond the neutrino field.Comment: 22 pages, 7 figure