Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions

We construct approximate initial data for non-spinning black hole binary systems by asymptotically matching the 4-metrics of two tidally perturbed Schwarzschild solutions in isotropic coordinates to a resummed post-Newtonian 4-metric in ADMTT coordinates. The specific matching procedure used here closely follows the calculation in gr-qc/0503011, and is performed in the so called buffer zone where both the post-Newtonian and the perturbed Schwarzschild approximations hold. The result is that both metrics agree in the buffer zone, up to the errors in the approximations. However, since isotropic coordinates are very similar to ADMTT coordinates, matching yields better results than in the previous calculation, where harmonic coordinates were used for the post-Newtonian 4-metric. In particular, not only does matching improve in the buffer zone, but due to the similarity between ADMTT and isotropic coordinates the two metrics are also close to each other near the black hole horizons. With the help of a transition function we also obtain a global smooth 4-metric which has errors on the order of the error introduced by the more accurate of the two approximations we match. This global smoothed out 4-metric is obtained in ADMTT coordinates which are not horizon penetrating. In addition, we construct a further coordinate transformation that takes the 4-metric from global ADMTT coordinates to new coordinates which are similar to Kerr-Schild coordinates near each black hole, but which remain ADMTT further away from the black holes. These new coordinates are horizon penetrating and lead, for example, to a lapse which is everywhere positive on the t=0 slice. Such coordinates may be more useful in numerical simulations.Comment: 25 pages, 21 figures. Replaced with accepted versio

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

Light Hadron Spectrum in the Instanton Liquid Model

We review our recent study of the role played by the chiral interactions induced by instantons, in the lowest-lying sector of the light hadron spectrum. We discuss how the ordering of the lowest meson and baryon excitations is explained by the structure of the instanton-induced quark-quark and gluon-gluon interaction. We focus on the pion, nucleon, vector- and axial-vector mesons, and on the scalar glueball. We find that all these hadrons are bound in this model and have realistic masses.Comment: 8 pages, talk given at "Hadron 07", XII International Conference on Hadron Spectroscopy, Frascati, October 8-13, 200

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

Feasibility of approximating spatial and local entanglement in long-range interacting systems using the extended Hubbard model

We investigate the extended Hubbard model as an approximation to the local and spatial entanglement of a one-dimensional chain of nanostructures where the particles interact via a long range interaction represented by a `soft' Coulomb potential. In the process we design a protocol to calculate the particle-particle spatial entanglement for the Hubbard model and show that, in striking contrast with the loss of spatial degrees of freedom, the predictions are reasonably accurate. We also compare results for the local entanglement with previous results found using a contact interaction (PRA, 81 (2010) 052321) and show that while the extended Hubbard model recovers a better agreement with the entanglement of a long-range interacting system, there remain realistic parameter regions where it fails to predict the quantitative and qualitative behaviour of the entanglement in the nanostructure system.Comment: 6 pages, 5 figures and 1 table; added results with correlated hopping term; accepted by EP

Binary black hole initial data from matched asymptotic expansions

We present an approximate metric for a binary black hole spacetime to construct initial data for numerical relativity. This metric is obtained by asymptotically matching a post-Newtonian metric for a binary system to a perturbed Schwarzschild metric for each hole. In the inner zone near each hole, the metric is given by the Schwarzschild solution plus a quadrupolar perturbation corresponding to an external tidal gravitational field. In the near zone, well outside each black hole but less than a reduced wavelength from the center of mass of the binary, the metric is given by a post-Newtonian expansion including the lowest-order deviations from flat spacetime. When the near zone overlaps each inner zone in a buffer zone, the post-Newtonian and perturbed Schwarzschild metrics can be asymptotically matched to each other. By demanding matching (over a 4-volume in the buffer zone) rather than patching (choosing a particular 2-surface in the buffer zone), we guarantee that the errors are small in all zones. The resulting piecewise metric is made formally $C^\infty$ with smooth transition functions so as to obtain the finite extrinsic curvature of a 3-slice. In addition to the metric and extrinsic curvature, we present explicit results for the lapse and the shift, which can be used as initial data for numerical simulations. This initial data is not accurate all the way to the asymptotically flat ends inside each hole, and therefore must be used with evolution codes which employ black hole excision rather than puncture methods. This paper lays the foundations of a method that can be sraightforwardly iterated to obtain initial data to higher perturbative order.Comment: 24 pages, 15 figures. Replaced with published version. Major editing of text, no major change to the physic

Strong decays of radially excited mesons in a chiral approach

We study radial excitations of pseudoscalar and vector (q bar q) mesons within a chiral approach. We derive a general form for a chiral Lagrangian describing processes involving excited pseudoscalar and vector mesons. The parameters of the chiral Lagrangian are fitted using data and previous calculations in the framework of the 3P0 model. Finite-width effects are examined and predictions for mesons previously not discussed are given. Available experimental data is analyzed whenever possible. Possible hints for exotic mesons and open interpretation-issues are discussed.Comment: 16 page

Many-particle interference beyond many-boson and many-fermion statistics

Identical particles exhibit correlations even in the absence of inter-particle interaction, due to the exchange (anti)symmetry of the many-particle wavefunction. Two fermions obey the Pauli principle and anti-bunch, whereas two bosons favor bunched, doubly occupied states. Here, we show that the collective interference of three or more particles leads to a much more diverse behavior than expected from the boson-fermion dichotomy known from quantum statistical mechanics. The emerging complexity of many-particle interference is tamed by a simple law for the strict suppression of events in the Bell multiport beam splitter. The law shows that counting events are governed by widely species-independent interference, such that bosons and fermions can even exhibit identical interference signatures, while their statistical character remains subordinate. Recent progress in the preparation of tailored many-particle states of bosonic and fermionic atoms promises experimental verification and applications in novel many-particle interferometers.Comment: 12 pages, 5 figure

A simple model for the vibrational modes in honeycomb lattices

The classical lattice dynamics of honeycomb lattices is studied in the harmonic approximation. Interactions between nearest neighbors are represented by springs connecting them. A short and necessary introduction of the lattice structure is presented. The dynamical matrix of the vibrational modes is then derived, and its eigenvalue problem is solved analytically. The solution may provide deeper insight into the nature of the vibrational modes. Numerical results for the vibrational frequencies are presented. To show that how effective our method used for the case of honeycomb lattice is, we also apply it to triangular and square lattice structures. A few suggested problems are listed in the concluding section.Comment: 9 pages, 12 figures, submitted to American Journal of Physic