Gauge-invariant variables in general-relativistic perturbations: globalization and zero-mode problem

An outline of a proof of the local decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime is briefly explained. We explicitly construct the gauge-invariant and gauge-variant parts of the linear metric perturbations based on some assumptions. We also point out the zero-mode problem is an essential problem to globalize of this decomposition of linear metric perturbations. The resolution of this zero-mode problem implies the possibility of the development of the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime in a global sense.Comment: (v1) 16 pages, no figure; (v2) 9 pages, no figure. Compactified for "2012 Awards for Essays on Gravitation" promoted by Gravity Research Foundation. References are deleted. no ingredients is changed. This version received Honorable Mention for 201

Critical comparison of electrode models in density functional theory based quantum transport calculations

We study the performance of two different electrode models in quantum transport calculations based on density functional theory: Parametrized Bethe lattices and quasi-one dimensional wires or nanowires. A detailed account of implementation details in both cases is given. From the systematic study of nanocontacts made of representative metallic elements, we can conclude that parametrized electrode models represent an excellent compromise between computational cost and electronic structure definition as long as the aim is to compare with experiments where the precise atomic structure of the electrodes is not relevant or defined with precision. The results obtained using parametrized Bethe lattices are essentially similar to the ones obtained with quasi one dimensional electrodes for large enough sections of these, adding a natural smearing to the transmission curves that mimics the true nature of polycrystalline electrodes. The latter are more demanding from the computational point of view, but present the advantage of expanding the range of applicability of transport calculations to situations where the electrodes have a well-defined atomic structure, as is case for carbon nanotubes, graphene nanoribbons or semiconducting nanowires. All the analysis is done with the help of codes developed by the authors which can be found in the quantum transport toolbox Alacant and are publicly available.Comment: 17 pages, 12 figure

Effective spin chains for fractional quantum Hall states

Fractional quantum Hall (FQH) states are topologically ordered which indicates that their essential properties are insensitive to smooth deformations of the manifold on which they are studied. Their microscopic Hamiltonian description, however, strongly depends on geometrical details. Recent work has shown how this dependence can be exploited to generate effective models that are both interesting in their own right and also provide further insight into the quantum Hall system. We review and expand on recent efforts to understand the FQH system close to the solvable thin-torus limit in terms of effective spin chains. In particular, we clarify how the difference between the bosonic and fermionic FQH states, which is not apparent in the thin-torus limit, can be seen at this level. Additionally, we discuss the relation of the Haldane-Shastry chain to the so-called QH circle limit and comment on its significance to recent entanglement studies.Comment: 6 pages, 5 figures. Written for a Special Issue on Foundations of Computational and Theoretical Nanoscience in Journal of Computational and Theoretical Nanoscience (proceedings for nanoPHYS'09 in Tokyo

Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains

We study a strong coupling expansion of the $\nu=1/3$ fractional quantum Hall state away from the Tao-Thouless limit and show that the leading quantum fluctuations lead to an effective spin-1 Hamiltonian that lacks parity symmetry. By analyzing the energetics, discrete symmetries of low-lying excitations, and string order parameters, we demonstrate that the $\nu=1/3$ fractional quantum Hall state is adiabatically connected to both Haldane and large-$D$ phases, and is characterized by a string order parameter which is dual to the ordinary one. This result indicates a close relation between (a generalized form of) the Haldane conjecture for spin chains and the fractional quantum Hall effect.Comment: 8 pages, 9 figure

Solid propulsion advanced concepts

The feasibility and application of a solid propulsion powered spacecraft concept to implement high energy missions independent of multiplanetary swingby opportunities are assessed and recommendations offered for future work. An upper stage, solid propulsion launch vehicle augmentation system was selected as the baseline configuration in view of the established program goals of low cost and high reliability. Spacecraft and propulsion system data that characterize mission performance capabilities were generated to serve as the basis for subsequent tradeoff studies. A cost effectiveness model was used for the preliminary feasibility assessment to provide a meaningful comparative effectiveness measure of the various candidate designs. The results substantiated the feasibility of the powered spacecraft concept when used in conjunction with several intermediate-sized launch vehicles as well as the existence of energy margins by which to exploit the attainment of extended mission capabilities. Additionally, in growth option applications, the employment of advanced propulsion systems and alternate spacecraft approaches appear promising

Toda Lattice and Tomimatsu-Sato Solutions

We discuss an analytic proof of a conjecture (Nakamura) that solutions of Toda molecule equation give those of Ernst equation giving Tomimatsu-Sato solutions of Einstein equation. Using Pfaffian identities it is shown for Weyl solutions completely and for generic cases partially.Comment: LaTeX 8 page

Gauge-invariant Formulation of the Second-order Cosmological Perturbations

Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. These equations imply that the tensor and the vector mode of the second order metric perturbations may be generated by the scalar-scalar mode coupling of the linear order perturbations as the result of the non-linear effects of the Einstein equations.Comment: 5 pages, no figure. RevTeX; short letter version of gr-qc/0605108; some details of explanations are adde