Goodness-of-fit tests in many dimensions

A method is presented to construct goodness-of-fit statistics in many dimensions for which the distribution of all possible test results in the limit of an infinite number of data becomes Gaussian if also the number of dimensions becomes infinite. Furthermore, an explicit example is presented, for which this distribution as good as only depends on the expectation value and the variance of the statistic for any dimension larger than one.Comment: 14 page

Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system

We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of Nn "nuclei" and Ne "electrons". We study the dependence of entanglement on the inter-particle interaction strength, on the number of particles, and on the particle masses. Consistent with kinematic intuition, the entanglement between two subsystems vanishes when the subsystems have very different masses, while it attains its maximal value for subsystems of comparable mass. We show how this entanglement feature can be inferred by means of the Born-Oppenheimer Ansatz, whose validity and breakdown can be understood from a quantum information point of view.Comment: Accepted in Eur. Phys. J. D (2014

Bosonic behavior of entangled fermions

Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi-composite-boson states. We derive the two-fermion-states that extremize the normalization ratio for a fixed single-fermion purity P, and establish general tight bounds for this indicator. For very small purities, P<1/N^2, the upper and lower bounds converge, which allows to quantify accurately the departure from perfectly bosonic behavior, for any state of many composite bosons.Comment: 9 pages, 5 figures, accepted by PR

A new numerical method to construct binary neutron star initial data

We present a new numerical method for the generation of binary neutron star initial data using a method along the lines of the the Wilson-Mathews or the closely related conformal thin sandwich approach. Our method uses six different computational domains, which include spatial infinity. Each domain has its own coordinates which are chosen such that the star surfaces always coincide with domain boundaries. These properties facilitate the imposition of boundary conditions. Since all our fields are smooth inside each domain, we are able to use an efficient pseudospectral method to solve the elliptic equations associated with the conformal thin sandwich approach. Currently we have implemented corotating configurations with arbitrary mass ratios, but an extension to arbitrary spins is possible. The main purpose of this paper is to introduce our new method and to test our code for several different configurations.Comment: 18 pages, 8 figures, 1 tabl

Black hole puncture initial data with realistic gravitational wave content

We present improved post-Newtonian-inspired initial data for non-spinning black-hole binaries, suitable for numerical evolution with punctures. We revisit the work of Tichy et al. [W. Tichy, B. Bruegmann, M. Campanelli, and P. Diener, Phys. Rev. D 67, 064008 (2003)], explicitly calculating the remaining integral terms. These terms improve accuracy in the far zone and, for the first time, include realistic gravitational waves in the initial data. We investigate the behavior of these data both at the center of mass and in the far zone, demonstrating agreement of the transverse-traceless parts of the new metric with quadrupole-approximation waveforms. These data can be used for numerical evolutions, enabling a direct connection between the merger waveforms and the post-Newtonian inspiral waveforms.Comment: 13 pages, 7 figures; replaced with published versio

A minimal no-radiation approximation to Einstein's field equations

An approximation to Einstein's field equations in Arnowitt-Deser-Misner (ADM) canonical formalism is presented which corresponds to the magneto-hydrodynamics (MHD) approximation in electrodynamics. It results in coupled elliptic equations which represent the maximum of elliptic-type structure of Einstein's theory and naturally generalizes previous conformal-flat truncations of the theory. The Hamiltonian, in this approximation, is identical with the non-dissipative part of the Einsteinian one through the third post-Newtonian order. The proposed scheme, where stationary spacetimes are exactly reproduced, should be useful to construct {\em realistic} initial data for general relativistic simulations as well as to model astrophysical scenarios, where gravitational radiation reaction can be neglected.Comment: 9 page

Constructing binary neutron star initial data with high spins, high compactnesses, and high mass ratios

The construction of accurate and consistent initial data for various binary parameters is a critical ingredient for numerical relativity simulations of the compact binary coalescence. In this article, we present an upgrade of the pseudospectral SGRID code, which enables us to access even larger regions of the binary neutron star parameter space. As a proof of principle, we present a selected set of first simulations based on initial configurations computed with the new code version. In particular, we simulate two millisecond pulsars close to their breakup spin, highly compact neutron stars with masses at about $98\%$ of the maximum supported mass of the employed equation of state, and an unequal mass systems with mass ratios even outside the range predicted by population synthesis models ($q = 2.03$). The discussed code extension will help us to simulate previously unexplored binary configurations. This is a necessary step to construct and test new gravitational wave approximants and to interpret upcoming binary neutron star merger observations. When we construct initial data, one has to specify various parameters, such as a rotation parameter for each star. Some of these parameters do not have direct physical meaning, which makes comparisons with other methods or models difficult. To facilitate this, we introduce simple estimates for the initial spin, momentum, mass, and center of mass of each individual star

High-accuracy high-mass ratio simulations for binary neutron stars and their comparison to existing waveform models

The subsequent observing runs of the advanced gravitational-wave detector network will likely provide us with various gravitational-wave observations of binary neutron star systems. For an accurate interpretation of these detections, we need reliable gravitational-wave models. To test and to point out how existing models could be improved, we perform a set of high-resolution numerical-relativity simulations for four different physical setups with mass ratios $q$ = $1.25$, $1.50$, $1.75$, $2.00$, and total gravitational mass $M = 2.7M_\odot$ . Each configuration is simulated with five different resolutions to allow a proper error assessment. Overall, we find approximately 2nd order converging results for the dominant $(2,2)$, but also subdominant $(2,1)$, $(3,3)$, $(4,4)$ modes, while, generally, the convergence order reduces slightly for an increasing mass ratio. Our simulations allow us to validate waveform models, where we find generally good agreement between state-of-the-art models and our data, and to prove that scaling relations for higher modes currently employed for binary black hole waveform modeling also apply for the tidal contribution. Finally, we also test if the current NRTidal model to describe tidal effects is a valid description for high-mass ratio systems. We hope that our simulation results can be used to further improve and test waveform models in preparation for the next observing runs

STUDY OF THE LEUKOCYTE MIGRATION INHIBITORY FACTOR IN HUMAN GLOMERULONEPHRITIS FROM THE ASPECT OF THE PROGNOSIS

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