Spatial and observational homogeneities of the galaxy distribution in standard cosmologies

This work discusses the possible empirical verification of the geometrical concept of homogeneity of the standard relativistic cosmology considering its various definitions of distance. We study the physical consequences of the distinction between the usual concept of spatial homogeneity (SH), as defined by the Cosmological Principle, and the concept of observational homogeneity (OH), arguing that OH is in principle falsifiable by means of astronomical observations, whereas verifying SH is only possible indirectly. Simulated counts of cosmological sources are produced by means of a generalized number-distance expression that can be specialized to produce either the counts of the Einstein-de Sitter (EdS) cosmology, which has SH by construction, or other types of counts, which do, or do not, have OH by construction. Expressions for observational volumes and differential densities are derived with the various cosmological distance definitions in the EdS model. Simulated counts that have OH by construction do not always exhibit SH features. The reverse situation is also true. Besides, simulated counts with no OH features at low redshift start showing OH characteristics at high redshift. The comoving distance seems to be the only distance definition where both SH and OH appear simultaneously. The results show that observations indicating possible lack of OH do not necessarily falsify the standard Friedmannian cosmology, meaning that this cosmology will not necessarily always produce observable homogeneous densities. The general conclusion is that the use of different cosmological distances in the characterization of the galaxy distribution lead to significant ambiguities in reaching conclusions about the behavior of the large-scale galaxy distribution in the Universe.Comment: 12 pages, 12 figures, LaTeX. Matches the final version sent to the journal. Accepted for publication in "Astronomy and Astrophysics

Zipf Law for Brazilian Cities

This work studies the Zipf Law for cities in Brazil. Data from censuses of 1970, 1980, 1991 and 2000 were used to select a sample containing only cities with 30,000 inhabitants or more. The results show that the population distribution in Brazilian cities does follow a power law similar to the ones found in other countries. Estimates of the power law exponent were found to be 2.22 +/- 0.34 for the 1970 and 1980 censuses, and 2.26 +/- 0.11 for censuses of 1991 and 2000. More accurate results were obtained with the maximum likelihood estimator, showing an exponent equal to 2.41 for 1970 and 2.36 for the other three years.Comment: 12 pages, 6 figures, 3 tables, Elsevier LaTeX, accepted for publication in "Physica A". Correction of minor mistyping (eq. 8

Generalized Chaplygin gas with α=0\alpha = 0 and the ΛCDM\Lambda CDM cosmological model

The generalized Chaplygin gas model is characterized by the equation of state $p = - \frac{A}{\rho^\alpha}$. It is generally stated that the case $\alpha = 0$ is equivalent to a model with cosmological constant and dust ($\Lambda CDM$). In this work we show that, if this is true for the background equations, this is not true for the perturbation equations. Hence, the mass spectrum predicted for both models may differ.Comment: Latex file, 4 pages, 2 figures in eps forma

Fast gates for ion traps by splitting laser pulses

We present a fast phase gate scheme that is experimentally achievable and has an operation time more than two orders of magnitude faster than current experimental schemes for low numbers of pulses. The gate time improves with the number of pulses following an inverse power law. Unlike implemented schemes which excite precise motional sidebands, thus limiting the gate timescale, our scheme excites multiple motional states using discrete ultra-fast pulses.We use beam-splitters to divide pulses into smaller components to overcome limitations due to the finite laser pulse repetition rate. This provides gate times faster than proposed theoretical schemes when we optimize a practical setup

Transport properties of a two impurity system: a theoretical approach

A system of two interacting cobalt atoms, at varying distances, was studied in a recent scanning tunneling microscope experiment by Bork et. al.[Nature Phys. 7, 901 (2011)]. We propose a microscopic model that explains, for all experimentally analyzed interatomic distances, the physics observed in these experiments. Our proposal is based on the two-impurity Anderson model, with the inclusion of a two-path geometry for charge transport. This many-body system is treated in the finite-U slave boson mean-field approximation and the logarithmic-discretization embedded-cluster approximation. We physically characterize the different charge transport regimes of this system at various interatomic distances and show that, as in the experiments, the features observed in the transport properties depend on the presence of two impurities but also on the existence of two conducting channels for electron transport. We interpret the splitting observed in the conductance as the result of the hybridization of the two Kondo resonances associated with each impurity.Comment: 5 pages, 5 figure

Electromagnetic response of high-Tc superconductors -- the slave-boson and doped-carrier theories

We evaluate the doping dependence of the quasiparticle current and low temperature superfluid density in two slave-particle theories of the tt't''J model -- the slave-boson theory and doped-carrier theory. In the slave-boson theory, the nodal quasiparticle current renormalization factor $\alpha$ vanishes proportionally to the zero temperature superfluid density $\rho_S(0)$; however, we find that away from the $\rho_S(0) \to 0$ limit $\alpha$ displays a much weaker doping dependence than $\rho_S(0)$. A similar conclusion applies to the doped-carrier theory, which differentiates the nodal and antinodal regions of momentum space. Due to its momentum space anisotropy, the doped-carrier theory enhances the value of $\alpha$ in the hole doped regime, bringing it to quantitative agreement with experiments, and reproduces the asymmetry between hole and electron doped cuprate superconductors. Finally, we use the doped-carrier theory to predict a specific experimental signature of local staggered spin correlations in doped Mott insulator superconductors which, we propose, should be observed in STM measurements of underdoped high-Tc compounds. This experimental signature distinguishes the doped-carrier theory from other candidate mean-field theories of high-Tc superconductors, like the slave-boson theory and the conventional BCS theory.Comment: 12 pages, RevTeX4, homepage http://dao.mit.edu/~we

Temperature effect on (2+1) experimental Kardar-Parisi-Zhang growth

We report on the effect of substrate temperature (T) on both local structure and long-wavelength fluctuations of polycrystalline CdTe thin films deposited on Si(001). A strong T-dependent mound evolution is observed and explained in terms of the energy barrier to inter-grain diffusion at grain boundaries, as corroborated by Monte Carlo simulations. This leads to transitions from uncorrelated growth to a crossover from random-to-correlated growth and transient anomalous scaling as T increases. Due to these finite-time effects, we were not able to determine the universality class of the system through the critical exponents. Nevertheless, we demonstrate that this can be circumvented by analyzing height, roughness and maximal height distributions, which allow us to prove that CdTe grows asymptotically according to the Kardar-Parisi-Zhang (KPZ) equation in a broad range of T. More important, one finds positive (negative) velocity excess in the growth at low (high) T, indicating that it is possible to control the KPZ non-linearity by adjusting the temperature.Comment: 6 pages, 5 figure

Magnetocaloric effect in integrable spin-s chains

We study the magnetocaloric effect for the integrable antiferromagnetic high-spin chain. We present an exact computation of the Gr\"uneisen parameter, which is closely related to the magnetocaloric effect, for the quantum spin-s chain on the thermodynamical limit by means of Bethe ansatz techniques and the quantum transfer matrix approach. We have also calculated the entropy S and the isentropes in the (H,T) plane. We have been able to identify the quantum critical points H_c^{(s)}=2/(s+1/2) looking at the isentropes and/or the characteristic behaviour of the Gr\"uneisen parameter.Comment: 6 pages, 3 figure