Joint Bayesian Estimation of Quasar Continua and the Lyman-Alpha Forest Flux Probability Distribution Function

We present a new Bayesian algorithm making use of Markov Chain Monte Carlo sampling that allows us to simultaneously estimate the unknown continuum level of each quasar in an ensemble of high-resolution spectra, as well as their common probability distribution function (PDF) for the transmitted Ly$\alpha$ forest flux. This fully automated PDF regulated continuum fitting method models the unknown quasar continuum with a linear Principal Component Analysis (PCA) basis, with the PCA coefficients treated as nuisance parameters. The method allows one to estimate parameters governing the thermal state of the intergalactic medium (IGM), such as the slope of the temperature-density relation $\gamma-1$, while marginalizing out continuum uncertainties in a fully Bayesian way. Using realistic mock quasar spectra created from a simplified semi-numerical model of the IGM, we show that this method recovers the underlying quasar continua to a precision of $\simeq7\%$ and $\simeq10\%$ at $z=3$ and $z=5$, respectively. Given the number of principal component spectra, this is comparable to the underlying accuracy of the PCA model itself. Most importantly, we show that we can achieve a nearly unbiased estimate of the slope $\gamma-1$ of the IGM temperature-density relation with a precision of $\pm8.6\%$ at $z=3$, $\pm6.1\%$ at $z=5$, for an ensemble of ten mock high-resolution quasar spectra. Applying this method to real quasar spectra and comparing to a more realistic IGM model from hydrodynamical simulations would enable precise measurements of the thermal and cosmological parameters governing the IGM, albeit with somewhat larger uncertainties given the increased flexibility of the model.Comment: 21 pages (+ Appendix), accepted at Ap

Supersolidity and phase diagram of softcore bosons in a triangular lattice

We study the softcore extended Bose Hubbard model in a two-dimensional triangular lattice by using the quantum Monte Carlo methods. The ground state phase diagram of the system exhibits a very fruitful structure. Except the Mott insulating state, four kinds of solid states with respect to the commensurate filling factors $\rho=1/3,2/3$ and $\rho=1$ are identified. Two of them (CDW II and CDW III) are newly predicted. In incommensurate fillings, superfluid, spuersolid as well as phase separation states are detected . As in the case for the hardcore bosons, a supersolid phase exists in $1/3<\rho<2/3$ while it is unstable towards the phase separation in $\rho<1/3$. However, this instability is refrained in $2/3<\rho<1$ due to the softening of the bosons and then a supersolid phase survives.Comment: 4 pages, 5 figure

Linear scaling computation of the Fock matrix. IX. Parallel computation of the Coulomb matrix

We present parallelization of a quantum-chemical tree-code [J. Chem. Phys. {\bf 106}, 5526 (1997)] for linear scaling computation of the Coulomb matrix. Equal time partition [J. Chem. Phys. {\bf 118}, 9128 (2003)] is used to load balance computation of the Coulomb matrix. Equal time partition is a measurement based algorithm for domain decomposition that exploits small variation of the density between self-consistent-field cycles to achieve load balance. Efficiency of the equal time partition is illustrated by several tests involving both finite and periodic systems. It is found that equal time partition is able to deliver 91 -- 98 % efficiency with 128 processors in the most time consuming part of the Coulomb matrix calculation. The current parallel quantum chemical tree code is able to deliver 63 -- 81% overall efficiency on 128 processors with fine grained parallelism (less than two heavy atoms per processor).Comment: 7 pages, 6 figure

Interlayer couplings and the coexistence of antiferromagnetic and d-wave pairing order in multilayer cuprates

A more extended low density region of coexisting uniform antiferromagnetism and d-wave superconductivity has been reported in multilayer cuprates, when compared to single or bilayer cuprates. This coexistence could be due to the enhanced screening of random potential modulations in inner layers or to the interlayer Heisenberg and Josephson couplings. A theoretical analysis using a renormalized mean field theory, favors the former explanation. The potential for an improved determination of the antiferromagnetic and superconducting order parameters in an ideal single layer from zero field NMR and infrared Josephson plasma resonances in multilayer cuprates is discussed.Comment: 6 pages, 2 figure

Theory for Gossamer and Resonating Valence Bond Superconductivity

We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed gossamer superconductivity. We formulate a renormalized mean field theory to approximately take into account the strong correlation effect in the partially projected Gutzwiller wavefucntions. At the half filled, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion U from a gossamer superconductor at small U. Away from the half filled,the Mott insulator is evolved into an resonating valence bond state, which is adiabatically connected to the gossamer superconductor.Comment: 10 pages, 13 figure