Compressibility of the Two-Dimensional infinite-U Hubbard Model

We study the interactions between the coherent quasiparticles and the incoherent Mott-Hubbard excitations and their effects on the low energy properties in the $U=\infty$ Hubbard model. Within the framework of a systematic large-N expansion, these effects first occur in the next to leading order in 1/N. We calculate the scattering phase shift and the free energy, and determine the quasiparticle weight Z, mass renormalization, and the compressibility. It is found that the compressibility is strongly renormalized and diverges at a critical doping $\delta_c=0.07\pm0.01$. We discuss the nature of this zero-temperature phase transition and its connection to phase separation and superconductivity.Comment: 4 pages, 3 eps figures, final version to appear in Phys. Rev. Let

A planar extrapolation of the correlation problem that permits pairing

It was observed previously that an SU(N) extension of the Hubbard model is dominated, at large N, by planar diagrams in the sense of 't Hooft, but the possibility of superconducting pairing got lost in this extrapolation. To allow for this possibility, we replace SU(N) by U(N,q), the unitary group in a vector space of quaternions. At the level of the free energy, the difference between the SU(N)and U(N,q) extrapolations appears only to first nonleading order in N.Comment: 8 pages, 2 figure

Some calculated effects of non-uniform inflow on the radiated noise of a large wind turbine

Far field computations were performed for a large wind turbine to evaluate the effects of non-uniform aerodynamic loading over the rotor disk. A modified version of the Farassat/Nystrom propeller noise prediction program was applied to account for the variations in loading due to inflow interruption by the upstream support tower. The computations indicate that for the uniform inflow case, relatively low noise levels are generated and the first rotational harmonic dominated the spectrum. For cases representing wake flow deficiences due to the tower structure, subtantially increased noise levels for all harmonics are indicated, the greatest increases being associated with the higher order harmonics

Improved Mean-Field Scheme for the Hubbard Model

Ground state energies and on-site density-density correlations are calculated for the 1-D Hubbard model using a linear combination of the Hubbard projection operators. The mean-field coefficients in the resulting linearized Equations of Motion (EOM) depend on both one-particle static expectation values as well as static two-particle correlations. To test the model, the one particle expectation values are determined self-consistently while using Lanczos determined values for the two particle correlation terms. Ground state energies and on-site density-density correlations are then compared as a function of $U$ to the corresponding Lanczos values on a 12 site Hubbard chain for 1/2 and 5/12 fillings. To further demonstrate the validity of the technique, the static correlation functions are also calculated using a similar EOM approach, which ignores the effective vertex corrections for this problem, and compares those results as well for a 1/2 filled chain. These results show marked improvement over standard mean-field techniques.Comment: 10 pages, 3 figures, text and figures as one postscript file -- does not need to be "TeX-ed". LA-UR-94-294

Ferromagnetism in the Periodic Anderson Model - a Modified Alloy Analogy

We introduce a new aproximation scheme for the periodic Anderson model (PAM). The modified alloy approximation represents an optimum alloy approximation for the strong coupling limit, which can be solved within the CPA-formalism. Zero-temperature and finite-temperature phase diagrams are presented for the PAM in the intermediate-valence regime. The diversity of magnetic properties accessible by variation of the system parameters can be studied by means of quasiparticle densities of states: The conduction band couples either ferro- or antiferromagneticaly to the f-levels. A finite hybridization is a necessary precondition for ferromagnetism. However, too strong hybridization generally suppresses ferromagnetism, but can for certain system parameters also lead to a semi-metallic state with unusual magnetic properties. By comparing with the spectral density approximation, the influence of quasiparticle damping can be examined.Comment: 20 pages, 13 figure

On Quantum Groups in the Hubbard Model with Phonons

The correct Hamiltonian for an extended Hubbard model with quantum group symmetry as introduced by A. Montorsi and M. Rasetti is derived for a D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a true quantum symmetry only for D = 1 and that terms of higher order in the fermionic operators in addition to phonons are required for a quantum symmetric hamiltonian. The condition for quantum symmetry is "half filling" and there is no local electron-phonon coupling. A discussion of Quantum symmetries in general is given in a formalism that should be readily accessible to non Hopf-algebraists.Comment: latex, 17 page

Strong-coupling expansions for the anharmonic Holstein model and for the Holstein-Hubbard model

A strong-coupling expansion is applied to the anharmonic Holstein model and to the Holstein-Hubbard model through fourth order in the hopping matrix element. Mean-field theory is then employed to determine transition temperatures of the effective (pseudospin) Hamiltonian. We find that anharmonic effects are not easily mimicked by an on-site Coulomb repulsion, and that anharmonicity strongly favors superconductivity relative to charge-density-wave order. Surprisingly, the phase diagram is strongly modified by relatively small values of the anharmonicity.Comment: 34 pages, typeset in ReVTeX, 11 encapsulated postscript files include

Mining Social Media Data to Study the Consequences of Dementia Diagnosis on Caregivers and Relatives

INTRODUCTION: Caregivers for people with dementia face a number of challenges such as changing family relationships, social isolation, or financial difficulties. Internet usage and social media are increasingly being recognised as resources to increase support and general public health. OBJECTIVE: Using automated analysis, the aim of this study was to explore (i) the age and sex of people who post to the social media forum Reddit about dementia diagnoses, (ii) the affected person and their diagnosis, (iii) which subreddits authors are posting to, (iv) the types of messages posted, and (v) the content of these posts. METHODS: We analysed Reddit posts concerning dementia diagnoses and used a previously developed text analysis pipeline to determine attributes of the posts and their authors. The posts were further examined through manual annotation of the diagnosis provided and the person affected. Lastly, we investigated the communities posters engage with and assessed the contents of the posts with an automated topic gathering/clustering technique. RESULTS: Five hundred and thirty-five Reddit posts were identified as relevant and further processed. The majority of posters in our dataset are females and predominantly close relatives, such as parents and grandparents, are mentioned. The communities frequented and topics gathered reflect not only the person's diagnosis but also potential outcomes, for example hardships experienced by the caregiver or the requirement for legal support. CONCLUSIONS: This work demonstrates the value of social media data as a resource for in-depth examination of caregivers' experience after a dementia diagnosis. It is important to study groups actively posting online, both in topic-specific and general communities, as they are most likely to benefit from novel internet-based support systems or interventions

Linked Cluster Expansion Around Mean-Field Theories of Interacting Electrons

A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field theories at weak (Hartree-Fock) and strong (Hubbard-III) coupling the expansion represents a universal and comprehensive tool for systematic improvements of static mean-field theories. As an example of the general formalism we investigate in detail an analytically tractable series of ring diagrams that correctly capture dynamical fluctuations at weak coupling. We introduce renormalizations of the diagrammatic expansion at various levels and show how the resultant theories are related to other approximations of similar origin. We demonstrate that only fully self-consistent approximations produce global and thermodynamically consistent extensions of static mean field theories. A fully self-consistent theory for the ring diagrams is reached by summing the so-called noncrossing diagrams.Comment: 17 pages, REVTEX, 13 uuencoded postscript figures in 2 separate file

Atmosphere, Interior, and Evolution of the Metal-Rich Transiting Planet HD 149026b

We investigate the atmosphere and interior of the new transiting planet HD 149026b, which appears to be very rich in heavy elements. We first compute model atmospheres at metallicities ranging from solar to ten times solar, and show how for cases with high metallicity or inefficient redistribution of energy from the day side, the planet may develop a hot stratosphere due to absorption of stellar flux by TiO and VO. The spectra predicted by these models are very different than cooler atmosphere models without stratospheres. The spectral effects are potentially detectable with the Spitzer Space Telescope. In addition the models with hot stratospheres lead to a large limb brightening, rather than darkening. We compare the atmosphere of HD 149026b to other well-known transiting planets, including the recently discovered HD 189733b, which we show have planet-to-star flux ratios twice that of HD 209458 and TrES-1. The methane abundance in the atmosphere of HD 189733b is a sensitive indicator of atmospheric temperature and metallicity and can be constrained with Spitzer IRAC observations. We then turn to interior studies of HD 149026b and use a grid of self-consistent model atmospheres and high-pressure equations of state for all components to compute thermal evolution models of the planet. We estimate that the mass of heavy elements within the planet is in the range of 60 to 93 M_earth. Finally, we discuss trends in the radii of transiting planets with metallicity in light of this new member of the class.Comment: Accepted to the Astrophysical Journal. 18 pages, including 10 figures. New section on the atmosphere of planet HD 189733b. Enhanced discussion of atmospheric Ti chemistry and core mass for HD 149026