Cluster Perturbation Theory for Hubbard models

Cluster perturbation theory is a technique for calculating the spectral weight of Hubbard models of strongly correlated electrons, which combines exact diagonalizations on small clusters with strong-coupling perturbation theory at leading order. It is exact in both the strong- and weak-coupling limits and provides a good approximation to the spectral function at any wavevector. Following the paper by S\'en\'echal et al. (Phys. Rev. Lett. {\bf 84}, 522 (2000)), we provide a more complete description and derivation of the method. We illustrate some of its capabilities, in particular regarding the effect of doping, the calculation of ground state energy and double occupancy, the disappearance of the Fermi surface in the $t-t'$ Hubbard model, and so on. The method is applicable to any model with on-site repulsion only.Comment: 11 pages, 10 figures (RevTeX 4

Third-order relativistic many-body calculations of energies and lifetimes of levels along the silver isoelectronic sequence

Energies of 5l_j (l= s, p, d, f, g) and 4f_j states in neutral Ag and Ag-like ions with nuclear charges Z = 48 - 100 are calculated using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates and lifetimes are calculated for the 17 possible 5l_j-5l'_{j'} and 4f_j-5l_{j'} electric-dipole transitions. Third-order corrections to energies and dipole matrix elements are included for neutral Ag and for ions with Z60. Comparisons are made with available experimental data for transition energies and lifetimes. Correlation energies and transition rates are shown graphically as functions of nuclear charge Z for selected cases. These calculations provide a theoretical benchmark for comparison with experiment and theory.Comment: 8 page

Endless microbes most beautiful and most wonderful

Since Antonie van Leeuwenhoek first observed microbes, we have come to learn that life on our planet includes not only the macroscopic lifeforms visible to the unaided eye that Charles Darwin studied but also an immense diversity of microbes (Fig 1). We have learned that microorganisms influence nearly every aspect of human existence with beneficial or detrimental effects. With their pivotal roles in biomass conversion, biogeochemical cycles, photosynthesis, and in promoting plant growth, life on this planet ultimately depends on the activities of microorganisms. On the other hand, microorganisms are the etiological agents of many diseases in humans, animals, and plants, causing massive economic losses yearly. Microorganisms also contribute significantly to the production of greenhouse gases such as CO2 and CH4 and, thus, contribute to global warming. In the past decade, we have also learned that microorganisms inhabiting the human body, i.e., the human microbiome, have profound effects on human physiology. Not to forget, some of our most delicious food products and beverages get their distinct qualities from microorganisms, and the pharmaceutical and biotechnological industry relies heavily on microbes. In terms of research, many technological breakthroughs in molecular biology, such as DNA cloning, PCR, and CRISPR-Cas technologies have their origin in microbes. Therefore, research in microbiology is as important now as it ever was

Effective Actions and Phase Fluctuations in d-wave Superconductors

We study effective actions for order parameter fluctuations at low temperature in layered d-wave superconductors such as the cuprates. The order parameter lives on the bonds of a square lattice and has two amplitude and two phase modes associated with it. The low frequency spectral weights for amplitude and relative phase fluctuations is determined and found to be subdominant to quasiparticle contributions. The Goldstone phase mode and its coupling to density fluctuations in charged systems is treated in a gauge-invariant manner. The Gaussian phase action is used to study both the $c$-axis Josephson plasmon and the more conventional in-plane plasmon in the cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum XY model, which incorporates important cutoff effects overlooked in previous studies. A variational analysis of this effective model shows that in the cuprates, quantum effects of phase fluctuations are important in reducing the zero temperature superfluid stiffness, but thermal effects are small for $T << T_c$.Comment: Some numerical estimates corrected and figures changed. to appear in PRB, Sept.1 (2000

Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases

We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.Comment: 18 pages, Latex, Revtex

Encoding and retrieval in a CA1 microcircuit model of the hippocampus

Recent years have witnessed a dramatic accumulation of knowledge about the morphological, physiological and molecular characteristics, as well as connectivity and synaptic properties of neurons in the mammalian hippocampus. Despite these advances, very little insight has been gained into the computational function of the different neuronal classes; in particular, the role of the various inhibitory interneurons in encoding and retrieval of information remains elusive. Mathematical and computational models of microcircuits play an instrumental role in exploring microcircuit functions and facilitate the dissection of operations performed by diverse inhibitory interneurons. A model of the CA1 microcircuitry is presented using biophysical representations of its major cell types: pyramidal, basket, axo-axonic, bistratified and oriens lacunosummoleculare cells. Computer simulations explore the biophysical mechanisms by which encoding and retrieval of spatio-temporal input patterns are achieved by the CA1 microcircuitry. The model proposes functional roles for the different classes of inhibitory interneurons in the encoding and retrieval cycles

Damping of phase fluctuations in superfluid Bose gases

Using Popov's hydrodynamic approach we derive an effective Euclidean action for the long-wavelength phase fluctuations of superfluid Bose gases in D dimensions. We then use this action to calculate the damping of phase fluctuations at zero temperature as a function of D. For D >1 and wavevectors | k | << 2 mc (where m is the mass of the bosons and c is the sound velocity) we find that the damping in units of the phonon energy E_k = c | k | is to leading order gamma_k / E_k = A_D (k_0^D / 2 pi rho) (| k | / k_0)^{2 D -2}, where rho is the boson density and k_0 =2 mc is the inverse healing length. For D -> 1 the numerical coefficient A_D vanishes and the damping is proportional to an additional power of |k | /k_0; a self-consistent calculation yields in this case gamma_k / E_k = 1.32 (k_0 / 2 pi rho)^{1/2} |k | / k_0. In one dimension, we also calculate the entire spectral function of phase fluctuations.Comment: 6 pages, 4 figures, published versio

Preschool Children and Behaviour Problems: A Prospective Study

Toddler/child behaviour problems have received relatively little previous attention. Prior studies have implicated a wide variety of factors in the aetiology of child behaviour problems but many of these factors are correlated and little is known about their independent contributions. Four broad categories of factors have been associated with child behaviour problems: (1) maternal social and economic characteristics; (2) maternal lifestyle; (3) maternal mental state/child-rearing practices; and (4) maternal and child physical health. The study took a sample of 5296 families from the Mater-University of Queensland Study of Pregnancy (MUSP) for whom 5-year prospective data are available. The major predictors of toddler behaviour problems were the mother's and child's health, and the mother's mental state. The mother's sociostructural characteristics and lifestyle made little or no additional contribution to the prediction models. It is, however, salutary to note that the majority of children who are classified as having high levels of troublesome behaviour do not fall into any of the risk categories. A variety of explanations and interpretations of the data is considered

Crossovers in Unitary Fermi Systems

Universality and crossover is described for attractive and repulsive interactions where, respectively, the BCS-BEC crossover takes place and a ferromagnetic phase transition is claimed. Crossovers are also described for optical lattices and multicomponent systems. The crossovers, universal parameters and phase transitions are described within the Leggett and NSR models and calculated in detail within the Jastrow-Slater approximation. The physics of ultracold Fermi atoms is applied to neutron, nuclear and quark matter, nuclei and electrons in solids whenever possible. Specifically, the differences between optical lattices and cuprates is discussed w.r.t. antiferromagnetic, d-wave superfluid phases and phase separation.Comment: 50 pages, 15 figures. Contribution to Lecture Notes in Physics "BCS-BEC crossover and the Unitary Fermi Gas" edited by W. Zwerge