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

Effects of Helium Phase Separation on the Evolution of Extrasolar Giant Planets

We build on recent new evolutionary models of Jupiter and Saturn and here extend our calculations to investigate the evolution of extrasolar giant planets of mass 0.15 to 3.0 M_J. Our inhomogeneous thermal history models show that the possible phase separation of helium from liquid metallic hydrogen in the deep interiors of these planets can lead to luminosities ~2 times greater than have been predicted by homogeneous models. For our chosen phase diagram this phase separation will begin to affect the planets' evolution at ~700 Myr for a 0.15 M_J object and ~10 Gyr for a 3.0 M_J object. We show how phase separation affects the luminosity, effective temperature, radii, and atmospheric helium mass fraction as a function of age for planets of various masses, with and without heavy element cores, and with and without the effect of modest stellar irradiation. This phase separation process will likely not affect giant planets within a few AU of their parent star, as these planets will cool to their equilibrium temperatures, determined by stellar heating, before the onset of phase separation. We discuss the detectability of these objects and the likelihood that the energy provided by helium phase separation can change the timescales for formation and settling of ammonia clouds by several Gyr. We discuss how correctly incorporating stellar irradiation into giant planet atmosphere and albedo modeling may lead to a consistent evolutionary history for Jupiter and Saturn.Comment: 22 pages, including 14 figures. Accepted to the Astrophysical Journa

Cumulant expansion of the periodic Anderson model in infinite dimension

The diagrammatic cumulant expansion for the periodic Anderson model with infinite Coulomb repulsion ($U=\infty$) is considered here for an hypercubic lattice of infinite dimension ($d=\infty$). The same type of simplifications obtained by Metzner for the cumulant expansion of the Hubbard model in the limit of $d=\infty$, are shown to be also valid for the periodic Anderson model.Comment: 13 pages, 7 figures.ps. To be published in J. Phys. A: Mathematical and General (1997

Sequence composition and environment effects on residue fluctuations in protein structures

The spectrum and scale of fluctuations in protein structures affect the range of cell phenomena, including stability of protein structures or their fragments, allosteric transitions and energy transfer. The study presents a statistical-thermodynamic analysis of relationship between the sequence composition and the distribution of residue fluctuations in protein-protein complexes. A one-node-per residue elastic network model accounting for the nonhomogeneous protein mass distribution and the inter-atomic interactions through the renormalized inter-residue potential is developed. Two factors, a protein mass distribution and a residue environment, were found to determine the scale of residue fluctuations. Surface residues undergo larger fluctuations than core residues, showing agreement with experimental observations. Ranking residues over the normalized scale of fluctuations yields a distinct classification of amino acids into three groups. The structural instability in proteins possibly relates to the high content of the highly fluctuating residues and a deficiency of the weakly fluctuating residues in irregular secondary structure elements (loops), chameleon sequences and disordered proteins. Strong correlation between residue fluctuations and the sequence composition of protein loops supports this hypothesis. Comparing fluctuations of binding site residues (interface residues) with other surface residues shows that, on average, the interface is more rigid than the rest of the protein surface and Gly, Ala, Ser, Cys, Leu and Trp have a propensity to form more stable docking patches on the interface. The findings have broad implications for understanding mechanisms of protein association and stability of protein structures.Comment: 8 pages, 4 figure

A generalization of moderated statistics to data adaptive semiparametric estimation in high-dimensional biology

The widespread availability of high-dimensional biological data has made the simultaneous screening of numerous biological characteristics a central statistical problem in computational biology. While the dimensionality of such datasets continues to increase, the problem of teasing out the effects of biomarkers in studies measuring baseline confounders while avoiding model misspecification remains only partially addressed. Efficient estimators constructed from data adaptive estimates of the data-generating distribution provide an avenue for avoiding model misspecification; however, in the context of high-dimensional problems requiring simultaneous estimation of numerous parameters, standard variance estimators have proven unstable, resulting in unreliable Type-I error control under standard multiple testing corrections. We present the formulation of a general approach for applying empirical Bayes shrinkage approaches to asymptotically linear estimators of parameters defined in the nonparametric model. The proposal applies existing shrinkage estimators to the estimated variance of the influence function, allowing for increased inferential stability in high-dimensional settings. A methodology for nonparametric variable importance analysis for use with high-dimensional biological datasets with modest sample sizes is introduced and the proposed technique is demonstrated to be robust in small samples even when relying on data adaptive estimators that eschew parametric forms. Use of the proposed variance moderation strategy in constructing stabilized variable importance measures of biomarkers is demonstrated by application to an observational study of occupational exposure. The result is a data adaptive approach for robustly uncovering stable associations in high-dimensional data with limited sample sizes

Many-body approach to the nonlinear interaction of charged particles with an interacting free electron gas

We report various many-body theoretical approaches to the nonlinear decay rate and energy loss of charged particles moving in an interacting free electron gas. These include perturbative formulations of the scattering matrix, the self-energy, and the induced electron density. Explicit expressions for these quantities are obtained, with inclusion of exchange and correlation effects.Comment: 11 pages, 5 figures. To appear in Journal of Physics

Exact Solution of a Electron System Combining Two Different t-J Models

A new strongly correlated electron model is presented. This is formed by two types of sites: one where double occupancy is forbidden, as in the t-J model, and the other where double occupancy is allowed but vacancy is not allowed, as an inverse t-J model. The Hamiltonian shows nearest and next-to-nearest neighbour interactions and it is solved by means of a modified algebraic nested Bethe Ansatz. The number of sites where vacancy is not allowed, may be treated as a new parameter if the model is looked at as a t-J model with impurities. The ground and excited states are described in the thermodynamic limit.Comment: Some corrections and references added. To be published in J. Phys.

Incommensurate antiferromagnetic fluctuations in the two-dimensional Hubbard model

Commensurate and incommensurate antiferromagnetic fluctuations in the two-dimensional repulsive t-t'-Hubbard model are investigated using functional renormalization group equations. For a sufficient deviation from half filling we establish the existence of local incommensurate order below a pseudocritical temperature T_{pc}. Fluctuations not accounted for in the mean field approximation are important--they lower T_{pc} by a factor \approx2.5.Comment: 7 pages, 8 figures, some changes due to referees' comments, equivalent to published versio

Strong-Coupling Expansion for the Hubbard Model

A strong-coupling expansion for models of correlated electrons in any dimension is presented. The method is applied to the Hubbard model in $d$ dimensions and compared with numerical results in $d=1$. Third order expansion of the Green function suffices to exhibit both the Mott metal-insulator transition and a low-temperature regime where antiferromagnetic correlations are strong. It is predicted that some of the weak photoemission signals observed in one-dimensional systems such as $SrCuO_2$ should become stronger as temperature increases away from the spin-charge separated state.Comment: 4 pages, RevTex, 3 epsf figures include

Breadboard stellar tracker system test report, volume 1

The performance of a star tracker equipped with a focal plane detector was evaluated. The CID board is an array of 256 x 256 pixels which are 20 x 20 micrometers in dimension. The tracker used for test was a breadboard tracker system developed by BASD. Unique acquisition and tracking algorithms are employed to enhance performance. A pattern recognition process is used to test for proper image spread function and to avoid false acquisition on noise. A very linear, high gain, interpixel transfer function is derived for interpolating star position. The lens used in the tracker has an EFL of 100 mm. The tracker has an FOV of 2.93 degrees resulting in a pixel angular subtense of 41.253 arc sec in each axis. The test procedure used for the program presented a star to the tracker in a circular pattern of positions; the pattern was formed by projecting a simulated star through a rotatable deviation wedge. Further tests determined readout noise, Noise Equivalent Displacement during track, and spatial noise during acquisition by taking related data and reducing it