119273967
Josephson effect in superconducting wires supporting multiple Majorana edge states
We study superconducting-normal-superconducting (SNS) Josephson junctions in one-dimensional topological superconductors which support more than one Majorana end mode. The variation of the energy spectrum with the superconducting phase is investigated by combining numerical diagonalizations of tight-binding models describing the SNS junction together with an analysis of appropriate low-energy effective Hamiltonians. We show that the four pi-periodicity characteristic of the fractional dc Josephson effect is preserved. Additionally, the ideal conductance of a NS junction with a topological supraconductor, hosting two Majorana modes at its ends, is doubled compared to the single Majorana case. Last, we illustrate how a nonzero superconducting phase gradient can potentially destroy the phases supporting multiple Majorana end states.
15453015
Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: toward a self-sustained topological Majorana phase.
We study a one-dimensional interacting electronic liquid coupled to a 1D array of classical magnetic moments and to a superconductor. We show that at low energy and temperature the magnetic moments and the electrons become strongly entangled and that a magnetic spiral structure emerges. For strong enough coupling between the electrons and magnetic moments, the 1D electronic liquid is driven into a topological superconducting phase supporting Majorana fermions without any fine-tuning of external parameters. Our analysis applies at low enough temperature to a quantum wire in proximity to a superconductor when the hyperfine interaction between electrons and nuclear spins is taken into account, or to a chain of magnetic adatoms adsorbed on a superconducting surface.
119500460
Coupled critical models: application to Ising-Potts models
Abstract We discuss the critical behaviour of 2 D Ising and q -states Potts models coupled by their energy density. We found new tricritical points. The procedure employed is the renormalisation approach of the perturbations series around conformal field theories representing pure models as already used for disordered spins models. This analysis could be useful to understand the physics of coupled critical models like the fully frustrated XY model.
124148859
2-D fractional supersymmetry: From rational to irrational conformal field theory
27849603
Universal ratios in the 2D tricritical ising model
We consider the universality class of the two-dimensional tricritical Ising model. The scaling form of the free energy leads to the definition of universal ratios of critical amplitudes which may have experimental relevance. We compute these universal ratios by a combined use of results coming from perturbed conformal field theory, integrable quantum field theory, and numerical methods.
119377774
2D FRACTIONAL SUPERSYMMETRY FOR RATIONAL CONFORMAL FIELD THEORY : APPLICATION FOR THIRD-INTEGER SPIN STATES
A 2D fractional supersymmetry theory is algebraically constructed. The Lagrangian is derived using an adapted superspace including, in addition to a scalar field, two fields with spins 13, 23 This theory turns out to be a rational conformal field theory. The symmetry of this model goes beyond the super-Virasoro algebra and connects these third-integer spin states. Besides the stress-momentum tensor, we obtain a supercurrent of spin 43. Cubic relations are involved in order to close the algebra; the basic algebra is no longer a Lie or a super-Lie algebra. The central charge of this model is found to be 53 Finally, we analyze the form that a local invariant action should take.
14997297
GaBoDS: the Garching-Bonn Deep Survey - III. Lyman-break galaxies in the Chandra Deep Field South
We present first results of our search for high-redshift galaxies in deep CCD mosaic images. As a pilot study for a larger survey, very deep images of the Chandra Deep Field South (CDFS), taken with WFI@MPG/ESO2.2m, are used to select large samples of 1070 U-band and 565 B-band dropouts with the Lyman-break method. The data of these Lyman-break galaxies are made public as an electronic table. These objects are good candidates for galaxies at z ∼ 3a ndz ∼ 4 which is supported by their photometric redshifts. The distributions of apparent magnitudes and the clustering properties of the two populations are analysed, and they show good agreement to earlier studies. We see no evolution in the comoving clustering scale length from z ∼ 3t oz ∼ 4. The techniques presented here will be applied to a much larger sample of U-dropouts from the whole survey in near future.
16212970
Relative clustering and the joint halo occupation distribution of red-sequence and blue-cloud galaxies in COMBO-17
This paper studies the relative spatial distribution of red-sequence and blue-cloud galaxies, and their relation to the dark matter distribution in the COMBO-17 survey as function of scale down to z ~ 1. We measure the second-order auto- and cross-correlation functions of galaxy clustering and express the relative biasing by using aperture statistics. Also estimated is the relation between the galaxies and the dark matter distribution exploiting galaxy-galaxy lensing (GGL). All observables are further interpreted in terms of a halo model. To fully explain the galaxy clustering cross-correlation function with a halo model, we introduce a new parameter, R, that describes the statistical correlation between numbers of red and blue galaxies within the same halo. We find that red and blue galaxies are clearly differently clustered, a significant evolution of the relative clustering with redshift is not found. There is evidence for a scale-dependence of relative biasing: the linear relative bias factor varies slightly between b ~ 1.7 ± 0.5 and ~2.2 ± 0.1 on spatial scales between roughly 100 h -1 kpc and 7h -1 Mpc, respectively. The linear correlation coefficient of galaxy number densities drops from a value near unity on large scales to r ~ 0.6 ± 0.15. Both biasing trends, the GGL and with some tension the galaxy numbers can be explained consistently within a halo model. Red galaxies typically start to populate haloes with masses starting from ≥10 12.1 ±0.2 h -1 M ⊙ , blue galaxies from ≥10 11.2±0.1 h -1 M ⊙ . For the cross-correlation function, one requires a halo occupation distribution (HOD) variance that becomes Poisson even for relatively small occupancy numbers. This rules out for our samples with high confidence a 'Poisson satellite' scenario, as found in semi-analytical models. We compare different model flavours, with and without galaxies at the halo centres, using Bayesian evidence. The result is inconclusive. However, red galaxies have to be concentrated towards the halo centre either by a red central galaxy or by a concentration parameter above that of dark matter. The value of R depends on the presence or absence of central galaxies: if no central galaxies or only red central galaxies are allowed, R is consistent with zero, whereas a positive correlation R = +0.5 ± 0.2 is needed if both blue and red galaxies can have central galaxies.
6695140
How accurate is Limber's equation?
Aims. The so-called Limber equation is widely used in the literature to relate the projected angular clustering of galaxies to the spatial clustering of galaxies in an approximate way. This note gives estimates of where the regime of applicability of Limber’s equation stops. Methods. This paper revisits Limber’s equation and compares its predictions to the accurate integral of which the Limber equation is an approximation for some realistic situations. Thereby, the accuracy of the approximation is quantified. Different cases of spatial correlation functions are considered. Results. Limber’s equation is accurate for small galaxy separations but breaks down beyond a certain separation that depends mainly on the ratio σ/rm and to some degree on the power-law index of spatial clustering; σ is the 1σ-width of the galaxy distribution in comoving distance ,a ndrm the mean comoving distance. Limber’s equation introduces a 10% systematic error that may be important at a scale of about a few degrees or in some cases, narrow galaxy distributions for example, even at arcmin scales. An alternative integral for such cases is given inside this paper.
119103864
The bispectrum covariance beyond Gaussianity - A log-normal approach
Context. To investigate and specify the statistical properties of cosmological fields with particular attention to possible non-Gaussian features, accurate formulae for the bispectrum and the bispectrum covariance are required. The bispectrum is the lowest-order statistic providing an estimate for non-Gaussianities of a distribution, and the bispectrum covariance depicts the errors of the bispectrum measurement and their correlation on different scales. Currently, there do exist fitting formulae for the bispectrum and an analytical expression for the bispectrum covariance, but the former is not very accurate and the latter contains several intricate terms and only one of them can be readily evaluated from the power spectrum of the studied field. Neglecting all higher-order terms results in the Gaussian approximation of the bispectrum covariance. Aims. We study the range of validity of this Gaussian approximation for two-dimensional non-Gaussian random fields. Methods. For this purpose, we simulate Gaussian and non-Gaussian random fields, the latter represented by log-normal fields and obtained directly from the former by a simple transformation. From the simulated fields, we calculate the power spectra, the bispectra, and the covariance from the sample variance of the bispectra, for different degrees of non-Gaussianity α, which is equivalent to the skewness on a given angular scale θg. In doing so, we minimize sample variance by selecting the same “phases” of the Gaussian and non-Gaussian fields. Results. We find that the Gaussian approximation of the bispectrum covariance provides a good approximation for degrees of nonGaussianity α ≤ 0.5 and a reasonably accurate approximation for α ≤ 1, both on scales >8θg. For larger values of α, the Gaussian approximation clearly breaks down. Using results from cosmic shear simulations, we estimate that the cosmic shear convergence fields are described by α < 0. 7a tθg ∼ 4 �� . Conclusions. We therefore conclude that the Gaussian approximation for the bispectrum covariance is likely to be applicable in ongoing and future cosmic shear studies.
8253626
The non-Gaussianity of the cosmic shear likelihood or How odd is the Chandra Deep Field South?
Aims. We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of σ8 really is as derived from the Chandra Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account, as well as the possibility of biases coming from the way the CDFS was selected. Methods. A brute force approach to estimating the likelihood from simulations must fail because of the high dimensionality of the problem. We therefore use independent component analysis to transform the cosmic shear correlation functions to a new basis, in which the likelihood approximately factorises into a product of one-dimensional distributions. Results. We find that the cosmic shear likelihood is significantly non-Gaussian. This leads to both a shift of the maximum of the posterior distribution and a significantly smaller credible region compared to the Gaussian case. We re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood in combination with conservative galaxy selection criteria that minimise calibration uncertainties. Assuming that the CDFS is a random pointing, we find σ8 = 0.68 +0.09 −0.16 for fixed Ωm = 0.25. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in ≈5% of the times. Taking biases into account arising from the way the CDFS was selected, which we model as being dependent on the number of haloes in the CDFS, we obtain σ8 = 0.71 +0.10 −0.15 . Combining the CDFS data with the parameter constraints from WMAP5 yields Ωm = 0.26 +0.03 −0.02 and σ8 = 0.79 +0.04 −0.03 for a flat universe.