Oxides,Oxides, and More Oxides: High-κ Oxides,Ferroelectrics, Ferromagnetics,and Multiferroics

We review and critique the recent developments on multifunctional oxide materials, which are gaining a good deal of interest. Recongnizing that this is a vast area, the focus of this treatment is mainly on high-κ dielectric, ferroelectric, magnetic, and multiferroic materials. Also, we consider ferrimagnetic oxides in the context of the new, rapidly developing field of negative-index metamaterials. This review is motivated by the recent resurgence of interest in complex oxides owing to their coupling of electrical, magnetic, thermal, mechanical, and optical properties, which make them suitable for a wide variety of applications, including heat, motion, electric, and magnetic sensors; tunable and compact microwave passive components; surface acoustic wave devices; nonlinear optics; and nonvolatile memory, and pave the way for designing multifunctional devices and unique applications in spintronics and negative refraction-index media. For most of the materials treated here, structural and physical properties, preparation methods accompanied by particulars of synthesis of thin films, devices based on them, and some projections into their future applications are discussed.     

Effects of pressure on structural,electronic, and mechanical properties of α,β,and γ uranium

The first-principles methods have been employed to calculate the structural, electronic, and mechanical properties of the α, β, and γ phases of uranium under pressure up to 100 GPa. The electronic structure has been viewed in forms of density of states and band structure. The mechanical stability of metal U in the α, β, and γ phases have been examined.The independent elastic constants, polycrystalline elastic moduli, as well as Poisson's ratio have been obtained. Upon compression, the elastic constants, elastic moduli, elastic wave velocities, and Debye temperature of α phase are enhanced pronouncedly. The value of B/G illustrates that α and γ phases are brittle in ground state.     

Preparation,characterization, and conductivity of YLnTiZrO7 (Ln = La,Nd, Sm,and Eu)

The pyrochlore oxide of composition YLnTiZrO₇ (Ln?=?La, Nd, Sm, and Eu) was prepared by sol–gel method. All the samples were characterized by powder X-ray diffraction (XRD), Raman, X-ray photoelectron spectroscopy (XPS), diffused reflectance spectroscopy, and impedance spectroscopy. The powder XRD and Raman studies reveal that these samples were crystallized in cubic lattice with pyrochlore structure. The Rietveld analysis of the samples was carried out to obtain the unit cell parameters and reliability factors. The broad Raman bands observed for all the samples are due to cation/anion disorder in the lattice and nanosize. The XPS analysis of the samples shows the characteristic peaks belonging to Y³⁺, Ln³⁺ (Ln?=?La, Nd, Sm, and Eu), Ti⁴⁺, and Zr⁴⁺. Electrical conductivity of YLaTiZrO₇ (YLTZ) and YEuTiZrO₇ (YETZ) samples was calculated from the impedance as a function of frequency and temperature. These samples have shown conductivity of the order of 10^?5 scm^?1 at 500 °C.     

Helmholtz, Riemann, and the Sirens: Sound, Color, and the “Problem of Space”

Emerging from music and the visual arts, questions about hearing and seeing deeply affected Hermann Helmholtz’s and Bernhard Riemann’s contributions to what became called the “problem of space [Raumproblem],” which in turn influenced Albert Einstein’s approach to general relativity. Helmholtz’s physiological investigations measured the time dependence of nerve conduction and mapped the three-dimensional manifold of color sensation. His concurrent studies on hearing illuminated musical evidence through experiments with mechanical sirens that connect audible with visible phenomena, especially how the concept of frequency unifies motion, velocity, and pitch. Riemann’s critique of Helmholtz’s work on hearing led Helmholtz to respond and study Riemann’s then-unpublished lecture on the foundations of geometry. During 1862–1870, Helmholtz applied his findings on the manifolds of hearing and seeing to the Raumproblem by supporting the quadratic distance relation Riemann had assumed as his fundamental hypothesis about geometrical space. Helmholtz also drew a “close analogy … in all essential relations between the musical scale and space.” These intersecting studies of hearing and seeing thus led to reconsideration and generalization of the very concept of “space,” which Einstein shaped into the general manifold of relativistic space-time.     

Densities and mixing volumes of mixtures of fluorobenzene, α,α,α-trifluorotoluene, tert-butylmethyl ether, and ethanol at temperature 298.15 K and pressure 0.1 MPa

The volumetric properties were evaluated from density data for the binary mixtures of (fluorobenzene + tert-butylmethyl ether), (α,α,α-trifluorotoluene + tert-butylmethyl ether), (tert-butylmethyl ether + ethanol), and the ternary mixtures of (fluorobenzene + tert-butylmethyl ether + ethanol) and (α,α,α-trifluorotoluene + tert-butylmethyl ether + ethanol). The observed densities were obtained by means of a vibrating-tube densimeter at the temperature 298.15 K and the pressure 101 kPa.The excess molar volumes of the ternary mixtures were estimated from binary solution data using several empirical equations with mean standard deviation less than 0.03 cm³·mol^-1. Stable chemical cross-associations among the molecules forming the mixtures were revealed.     

Eigenvalues, Peres＇ Separability Condition, and Entanglement

The general expression with the physical significance and positive-definite condition of the eigenvalues of 4×4 Hermitian and trace-one matrix are obtained. The obvious expression of Peres' separability condition for an arbitrary state of two qubits is then given and its operational feature is enhanced. Furthermore, we discuss some applications to the calculation of the entanglement, the upper bound of the entanglement, and a model of the transfer of entanglement in a qubit chain with noise.     

Nanomagnetism:Principles,nanostructures,and biomedical applications

Nanomagnetism is the origin of many unique properties in magnetic nanomaterials that can be used as building blocks in information technology, spintronics, and biomedicine. Progresses in nanomagnetic principles, distinct magnetic nanostructures, and the biomedical applications of nanomagnetism are summarized.     

Hitchin–Kobayashi Correspondence, Quivers, and Vortices

 A twisted quiver bundle is a set of holomorphic vector bundles over a complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collection of holomorphic vector bundles, labelled by the arrows. When the manifold is K?hler, quiver bundles admit natural gauge-theoretic equations, which unify many known equations for bundles with extra structure. In this paper we prove a Hitchin–Kobayashi correspondence for twisted quiver bundles over a compact K?hler manifold, relating the existence of solutions to the gauge equations to a stability criterion, and consider its application to a number of situations related to Higgs bundles and dimensional reductions of the Hermitian–Einstein equations. Received: 10 December 2001 / Accepted: 10 November 2002 Published online: 28 May 2003 RID="⋆" ID="⋆" Current address: Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK. E-mail:L.Alvarez-Consul@maths.bath.ac.uk RID="⋆⋆" ID="⋆⋆" Current address: Instituto de Matemáticas y Física Fundamental, CSIC, Serrano 113 bis, 28006 Madrid, Spain. E-mail:oscar.garcia-prada@uam.es Communicated by R.H. Dijkgraaf     

Cartan–Weyl Dirac and Laplacian Operators,Brownian Motions: The Quantum Potential and Scalar Curvature,Maxwell’s and Dirac-Hestenes Equations,and Supersymmetric Systems

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q