A General Method for Complete Population Transfer in Degenerate Systems

A simple theoretical solution to the design of a control field that generates complete population transfer from an initial state, via $N$ nondegenerate intermediate states, to one arbitrary member of $M$ ($M\leq N$) degenerate states is constructed. The full control field exploits an $(M+N-1)$-node null adiabatic state, created by designing the relative phases and amplitudes of the component fields that together make up the full field. The solution found is universal in the sense that it does not depend on the exact number of the unwanted degenerate states or their properties. The results obtained suggest that a class of multi-level quantum systems with degenerate states can be completely controllable, even under extremely strong constraints, e.g., never populating a Hilbert subspace that is only a few dimensions smaller than the whole Hilbert space.Comment: 12 pages, 5 figures, submitted to Phys. Rev.

Multiexciton molecules in the hexaborides

We investigate multiexciton bound states in a semiconducting phase of divalent hexaborides. Due to three degenerate valleys in both the conduction and valence bands the binding energy of a 6-exciton molecule is greatly enhanced by the shell effect. The ground state energies of multiexciton molecules are calculated using the density functional formalism. We also show that charged impurities stabilize multiexciton complexes leading to condensation of localized excitons. These complexes can act as nucleation centers of local moments.Comment: RevTEX, 7 pages with 3 figure

Landau-Fermi liquid analysis of the 2D t-t' Hubbard model

We calculate the Landau interaction function f(k,k') for the two-dimensional t-t' Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface.Comment: 10 pages, 16 figure

Star Formation Around Super-Massive Black Holes

The presence of young massive stars orbiting on eccentric rings within a few tenths of a parsec of the supermassive black hole in the Galactic centre is challenging for theories of star formation. The high tidal shear from the black hole should tear apart the molecular clouds that form stars elsewhere in the Galaxy, while transporting the stars to the Galactic centre also appears unlikely during their stellar lifetimes. We present numerical simulations of the infall of a giant molecular cloud that interacts with the black hole. The transfer of energy during closest approach allows part of the cloud to become bound to the black hole, forming an eccentric disc that quickly fragments to form stars. Compressional heating due to the black hole raises the temperature of the gas to 100-1000K, ensuring that the fragmentation produces relatively high stellar masses. These stars retain the eccentricity of the disc and, for a sufficiently massive initial cloud, produce an extremely top-heavy distribution of stellar masses. This potentially repetitive process can therefore explain the presence of multiple eccentric rings of young stars in the presence of a supermassive black hole.Comment: 20 pages includingh 7 figures. "This is the author's version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science, 321, (22 August 2008), doi:10.1126/science.1160653". Reprints and animations can be found at http://star-www.st-and.ac.uk/~iab1

Model-robust regression and a Bayesian ``sandwich'' estimator

We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber--White sandwich estimator. The sandwich estimator is known to provide asymptotically correct frequentist inference, even when standard modeling assumptions such as linearity and homoscedasticity in the data-generating mechanism are violated. Our derivation provides a compelling Bayesian justification for using this simple and popular tool, and it also clarifies what is being estimated when the data-generating mechanism is not linear. We demonstrate the applicability of our approach using a simulation study and health care cost data from an evaluation of the Washington State Basic Health Plan.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS362 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Magnetic Response in the Underdoped Cuprates

We examine the dynamical magnetic response of the underdoped cuprates by employing a phenomenological theory of a doped resonant valence bond state where the Fermi surface is truncated into four pockets. This theory predicts a resonant spin response which with increasing energy (0 to 100meV) appears as an hourglass. The very low energy spin response is found at (pi,pi +- delta) and (pi +- delta,pi) and is determined by scattering from the pockets' frontside to the tips of opposite pockets where a van Hove singularity resides. At energies beyond 100 meV, strong scattering is seen from (pi,0) to (pi,pi). This theory thus provides a semi-quantitative description of the spin response seen in both INS and RIXS experiments at all relevant energy scales

Bichromatically driven double well: parametric perspective of the strong-field control landscape reveals the influence of chaotic states

The aim of this work is to understand the influence of chaotic states in control problems involving strong fields. Towards this end, we numerically construct and study the strong field control landscape of a bichromatically driven double well. A novel measure based on correlating the overlap intensities between Floquet states and an initial phase space coherent state with the parametric motion of the quasienergies is used to construct and interpret the landscape features. "Walls" of no control, robust under variations of the relative phase between the fields, are seen on the control landscape and associated with multilevel interactions involving chaotic Floquet states.Comment: 9 pages and 6 figures. Rewritten and expanded version of arXiv:0707.4547 [nlin.CD]. Accepted for publication in J. Chem. Phys. (2008

Disproportionation and electronic phase separation in parent manganite LaMnO_3

Nominally pure undoped parent manganite LaMnO_3 exhibits a puzzling behavior inconsistent with a simple picture of an A-type antiferromagnetic insulator (A-AFI) with a cooperative Jahn-Teller ordering. We do assign its anomalous properties to charge transfer instabilities and competition between insulating A-AFI phase and metallic-like dynamically disproportionated phase formally separated by a first-order phase transition at T_{disp}=T_{JT}\approx 750 K. The unconventional high-temperature phase is addressed to be a specific electron-hole Bose liquid (EHBL) rather than a simple "chemically" disproportionated R(Mn^{2+}Mn^{4+})O_3 phase. New phase does nucleate as a result of the charge transfer (CT) instability and evolves from the self-trapped CT excitons, or specific EH-dimers, which seem to be a precursor of both insulating and metallic-like ferromagnetic phases observed in manganites. We arrive at highly frustrated system of triplet (e_g^2)^3A_{2g} bosons moving in a lattice formed by hole Mn^{4+} centers. Starting with different experimental data we have reproduced a typical temperature dependence of the volume fraction of high-temperature mixed-valent EHBL phase. We argue that a slight nonisovalent substitution, photo-irradiation, external pressure or magnetic field gives rise to an electronic phase separation with a nucleation or an overgrowth of EH-droplets. Such a scenario provides a comprehensive explanation of numerous puzzling properties observed in parent and nonisovalently doped manganite LaMnO_3 including an intriguing manifestation of superconducting fluctuations.Comment: 20 pages, 8 figure

Kaolinite-catalyzed air oxidation of hydrazine: Consideration of several compositional, structural and energetic factors in surface activation

Clay minerals have been shown to have numerous, curious, energetic properties by virtue of ultra-violet light release which can be triggered by gentle environmental changes such as wetting and dewetting by a variety of liquids, unique among them water and hydrazine. Since both water and hydrazine play multiple key roles in the air-oxidation of hydrazine on kaolinite surfaces, this reaction would seem to have prime potential for studying interrelationships of energy storage, release and chemical reactivity of clay surfaces, capacities basic to either the Bernal or Cairns-Smith roles of minerals in the origin of life. Establishment of the capacity for stored electronic energy to significantly alter surface chemistry is important, regardless of the reaction chosen to demonstrate it. Hydrazine air oxidation is overawingly complex, given the possibilities for step-wise control and monitoring of parameters. In the light of recently extended characterization of the kaolinite and model sheet catalysts we used to study hydrazine oxidation and gamma-irradiated silica, previous studies of hydrazine air-oxidation on aluminosilicate surfaces have been reevaluated. Our former conclusion remains intact that, whereas trace structural and surface contaminants do play some role in the catalysis of oxidation, they are not the only, nor even the dominant, catalytic centers. Initial intermediates in the oxidation can now be proposed which are consistent with production via O(-)-centers as well as ferric iron centers. The greater than square dependence of the initial reaction rate on the weight of the clay is discussed in the light of these various mechanistic possibilities