Sodium vacancy ordering and the co-existence of localized spins and itinerant charges in NaxCoO2

The sodium cobaltate family (NaxCoO2) is unique among transition metal oxides because the Co sits on a triangular lattice and its valence can be tuned over a wide range by varying the Na concentration x. Up to now detailed modeling of the rich phenomenology (which ranges from unconventional superconductivity to enhanced thermopower) has been hampered by the difficulty of controlling pure phases. We discovered that certain Na concentrations are specially stable and are associated with superlattice ordering of the Na clusters. This leads naturally to a picture of co-existence of localized spins and itinerant charge carriers. For x = 0.84 we found a remarkably small Fermi energy of 87 K. Our picture brings coherence to a variety of measurements ranging from NMR to optical to thermal transport. Our results also allow us to take the first step towards modeling the mysterious ``Curie-Weiss'' metal state at x = 0.71. We suggest the local moments may form a quantum spin liquid state and we propose experimental test of our hypothesis.Comment: 16 pages, 5 figure

Quantum planes and quantum cylinders from Poisson homogeneous spaces

Quantum planes and a new quantum cylinder are obtained as quantization of Poisson homogeneous spaces of two different Poisson structures on classical Euclidean group E(2).Comment: 13 pages, plain Tex, no figure

Imaging nonequilibrium atomic vibrations with x-ray diffuse scattering

For over a century, x-ray scattering has been the most powerful tool for determining the equilibrium structure of crystalline materials. Deviations from perfect periodicity, for example due to thermal motion of the atoms, reduces the intensity of the Bragg peaks as well as produces structure in the diffuse scattering background. Analysis of the thermal diffuse scattering (TDS) had been used to determine interatomic force constants and phonon dispersion in relatively simple cases before inelastic neutron scattering became the preferred technique to study lattice dynamics. With the advent of intense synchrotron x-ray sources, there was a renewed interest in TDS for measuring phonon dispersion. The relatively short x-ray pulses emanating from these sources also enables the measurement of phonon dynamics in the time domain. Prior experiments on nonequilibrium phonons were either limited by time-resolution and/or to relatively long wavelength excitations. Here we present the first images of nonequilibrium phonons throughout the Brillouin zone in photoexcited III-V semiconductors, indium-phosphide and indium-antimonide, using picosecond time-resolved diffuse scattering. In each case, we find that the lattice remain out of equilibrium for several hundred picoseconds up to nanoseconds after laser excitation. The non-equilibrium population is dominated by transverse acoustic phonons which in InP are directed along high-symmetry directions. The results have wide implications for the detailed study of electron-phonon and phonon-phonon coupling in solids.Comment: 10 pages, 3 figure

Flux through a hole from a shaken granular medium

We have measured the flux of grains from a hole in the bottom of a shaken container of grains. We find that the peak velocity of the vibration, vmax, controls the flux, i.e., the flux is nearly independent of the frequency and acceleration amplitude for a given value of vmax. The flux decreases with increasing peak velocity and then becomes almost constant for the largest values of vmax. The data at low peak velocity can be quantitatively described by a simple model, but the crossover to nearly constant flux at larger peak velocity suggests a regime in which the granular density near the container bottom is independent of the energy input to the system.Comment: 14 pages, 4 figures. to appear in Physical Review

The PARSE Programming Paradigm. Part I: Software Development Methodology. Part II: Software Development Support Tools

The programming methodology of PARSE (parallel software environment), a software environment being developed for reconfigurable non-shared memory parallel computers, is described. This environment will consist of an integrated collection of language interfaces, automatic and semi-automatic debugging and analysis tools, and operating system —all of which are made more flexible by the use of a knowledge-based implementation for the tools that make up PARSE. The programming paradigm supports the user freely choosing among three basic approaches /abstractions for programming a parallel machine: logic-based descriptive, sequential-control procedural, and parallel-control procedural programming. All of these result in efficient parallel execution. The current work discusses the methodology underlying PARSE, whereas the companion paper, “The PARSE Programming Paradigm — II: Software Development Support Tools,” details each of the component tools

Quantized algebras of functions on homogeneous spaces with Poisson stabilizers

Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0<q<1. We study a quantization C(G_q/K_q) of the algebra of continuous functions on G/K. Using results of Soibelman and Dijkhuizen-Stokman we classify the irreducible representations of C(G_q/K_q) and obtain a composition series for C(G_q/K_q). We describe closures of the symplectic leaves of G/K refining the well-known description in the case of flag manifolds in terms of the Bruhat order. We then show that the same rules describe the topology on the spectrum of C(G_q/K_q). Next we show that the family of C*-algebras C(G_q/K_q), 0<q\le1, has a canonical structure of a continuous field of C*-algebras and provides a strict deformation quantization of the Poisson algebra \C[G/K]. Finally, extending a result of Nagy, we show that C(G_q/K_q) is canonically KK-equivalent to C(G/K).Comment: 23 pages; minor changes, typos correcte

Quantum teardrops

Algebras of functions on quantum weighted projective spaces are introduced, and the structure of quantum weighted projective lines or quantum teardrops are described in detail. In particular the presentation of the coordinate algebra of the quantum teardrop in terms of generators and relations and classification of irreducible *-representations are derived. The algebras are then analysed from the point of view of Hopf-Galois theory or the theory of quantum principal bundles. Fredholm modules and associated traces are constructed. C*-algebras of continuous functions on quantum weighted projective lines are described and their K-groups computed.Comment: 18 page

An Empirical Charge Transfer Potential with Correct Dissociation Limits

The empirical valence bond (EVB) method [J. Chem. Phys. 52, 1262 (1970)] has always embodied charge transfer processes. The mechanism of that behavior is examined here and recast for use as a new empirical potential energy surface for large-scale simulations. A two-state model is explored. The main features of the model are: (1) Explicit decomposition of the total system electron density is invoked; (2) The charge is defined through the density decomposition into constituent contributions; (3) The charge transfer behavior is controlled through the resonance energy matrix elements which cannot be ignored; and (4) A reference-state approach, similar in spirit to the EVB method, is used to define the resonance state energy contributions in terms of "knowable" quantities. With equal validity, the new potential energy can be expressed as a nonthermal ensemble average with a nonlinear but analytical charge dependence in the occupation number. Dissociation to neutral species for a gas-phase process is preserved. A variant of constrained search density functional theory is advocated as the preferred way to define an energy for a given charge.Comment: Submitted to J. Chem. Phys. 11/12/03. 14 pages, 8 figure