Ginzburg-Landau Like Theory for High Temperature Superconductivity in the Cuprates: Emergent d-wave Order

High temperature superconductivity in the cuprates remains one of the most widely investigated, constantly surprising, and poorly understood phenomena in physics. Here, we describe briefly a new phenomenological theory inspired by the celebrated description of superconductivity due to Ginzburg and Landau and believed to describe its essence. This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. We propose, for superconducting cuprates, a similar functional of the complex, in plane, nearest neighbor spin singlet bond (or Cooper) pair amplitude psi_ij. A crucial part of it is a (short range) positive interaction between nearest neighbor bond pairs, of strength J'. Such an interaction leads to nonzero long wavelength phase stiffness or superconductive long range order, with the observed d-wave symmetry, below a temperature T_c\simzJ' where z is the number of nearest neighbours; it is thus an emergent, collective consequence. Using the functional, we calculate a large range of properties, e.g. the pseudogap transition temperature T* as a function of hole doping x, the transition curve T_c(x), the superfluid stiffness rho_s(x,T), the specific heat (without and with a magnetic field) due to the fluctuating pair degrees of freedom, and the zero temperature vortex structure. We find remarkable agreement with experiment. We also calculate the self energy of electrons hopping on the square cuprate lattice and coupled to electrons of nearly opposite momenta via inevitable long wavelength Cooper pair fluctuations formed of these electrons. The ensuing results for electron spectral density are successfully compared with recent ARPES experiments, and comprehensively explain strange features such as temperature dependent Fermi arcs above T_c and the 'bending' of the superconducting gap below T_c .Comment: 22 pages, 14 figures, to appear in Int J Mod Phys

The diagnostic value of synovial histopathology in undifferentiated inflammatory arthritis: a prospective study in 154 consecutive patients

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Cosmic Structure and Dynamics of the Local Universe

We present a cosmography analysis of the Local Universe based on the recently released Two-Micron All-Sky Redshift Survey (2MRS). Our method is based on a Bayesian Networks Machine Learning algorithm (the Kigen-code) which self-consistently samples the initial density fluctuations compatible with the observed galaxy distribution and a structure formation model given by second order Lagrangian perturbation theory (2LPT). From the initial conditions we obtain an ensemble of reconstructed density and peculiar velocity fields which characterize the local cosmic structure with high accuracy unveiling nonlinear structures like filaments and voids in detail. Coherent redshift space distortions are consistently corrected within 2LPT. From the ensemble of cross-correlations between the reconstructions and the galaxy field and the variance of the recovered density fields we find that our method is extremely accurate up to k ~ 1 h Mpc^-1 and still yields reliable results down to scales of about 3-4 h^-1 Mpc. The motion of the local group we obtain within ~ 80 h^-1 Mpc (v_LG=522+-86 km s^-1, l_LG=291^o +- 16^o, b_LG=34^o+-8^o) is in good agreement with measurements derived from the CMB and from direct observations of peculiar motions and is consistent with the predictions of LambdaCDM.Comment: 6 pages, 5 figures; accepted at MNRAS after minor correction

Deprojection of galaxy cluster X-ray, Sunyaev-Zeldovich temperature decrement, and weak-lensing mass maps

A general method of deprojecting two-dimensional images to reconstruct the three-dimensional structure of the projected object (specifically, X-ray, Sunyaev-Zeldovich [SZ], and gravitational lensing maps of rich clusters of galaxies), assuming axial symmetry, is considered. Here we test the applicability of the method for realistic, numerically simulated galaxy clusters, viewed from three orthogonal projections at four redshift outputs. We demonstrate that the assumption of axial symmetry is a good approximation for the three-dimensional structure in this ensemble of galaxy clusters. Applying the method, we demonstrate that a unique determination of the cluster inclination angle is possible from comparison between the SZ and X-ray images and, independently, between SZ and surface density maps. Moreover, the results from these comparisons are found to be consistent with each other and with the full three-dimensional structure inclination angle determination. The radial dark matter and gas density profiles as calculated from the actual and reconstructed three-dimensional distributions show a very good agreement. The method is also shown to provide a direct determination of the baryon fraction in clusters, independent of the cluster inclination angle.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/60622/1/Zaroubi2000Deprojection.pd

ZOBOV: a parameter-free void-finding algorithm

ZOBOV (ZOnes Bordering On Voidness) is an algorithm that finds density depressions in a set of points, without any free parameters, or assumptions about shape. It uses the Voronoi tessellation to estimate densities, which it uses to find both voids and subvoids. It also measures probabilities that each void or subvoid arises from Poisson fluctuations. This paper describes the ZOBOV algorithm, and the results from its application to the dark-matter particles in a region of the Millennium Simulation. Additionally, the paper points out an interesting high-density peak in the probability distribution of dark-matter particle densities.Comment: 10 pages, 8 figures, MNRAS, accepted. Added explanatory figures, and better edge-detection methods. ZOBOV code available at http://www.ifa.hawaii.edu/~neyrinck/vobo

Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices

A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind encountered in quantum physics the memory and CPU requirements of this method scale linearly with the dimension of the matrix. We derive a rigorous estimate of the statistical error, supporting earlier observations that the computational efficiency of this approach increases with matrix size. We use this method and an imaginary-time version of it to compute the energy and the specific heat of three different, exactly solvable, spin-1/2 models and compare with the exact results to study the dependence of the statistical errors on sample and matrix size.Comment: 24 pages, 24 figure