Resonant recoil in extreme mass ratio binary black hole mergers

The inspiral and merger of a binary black hole system generally leads to an asymmetric distribution of emitted radiation, and hence a recoil of the remnant black hole directed opposite to the net linear momentum radiated. The recoil velocity is generally largest for comparable mass black holes and particular spin configurations, and approaches zero in the extreme mass ratio limit. It is generally believed that for extreme mass ratios eta<<1, the scaling of the recoil velocity is V {\propto} eta^2, where the proportionality coefficient depends on the spin of the larger hole and the geometry of the system (e.g. orbital inclination). Here we show that for low but nonzero inclination prograde orbits and very rapidly spinning large holes (spin parameter a*>0.9678) the inspiralling binary can pass through resonances where the orbit-averaged radiation-reaction force is nonzero. These resonance crossings lead to a new contribution to the kick, V {\propto} eta^{3/2}. For these configurations and sufficiently extreme mass ratios, this resonant recoil is dominant. While it seems doubtful that the resonant recoil will be astrophysically significant, its existence suggests caution when extrapolating the results of numerical kick results to extreme mass ratios and near-maximal spins.Comment: fixed references; matches PRD accepted version (minor revision); 9 pages, 2 figure

UV and X-ray Spectral Lines of FeXXIII Ion for Plasma Diagnostics

We have calculated X-ray and UV spectra of Be-like Fe (FeXXIII) ion in collisional-radiative model including all fine-structure transitions among the 2s^2, 2s2p, 2p^2, 2snl, and 2pnl levels where n=3 and 4, adopting data for the collision strengths by Zhang & Sampson (1992) and by Sampson, Goett, & Clark (1984). Some line intensity ratios can be used for the temperature diagnostics. We show 5 ratios in UV region and 9 ratios in X-ray region as a function of electron temperature and density at 0.3keV < T_e < 10keV and $n_e = 1 - 10^{25} cm^{-3}$. The effect of cascade in these line ratios and in the level population densities are discussed.Comment: LaTeX, 18 pages, 10 Postscript figures. To appear in Physica Script

NMR evidence for two-step phase-separation in Nd_{1.85}Ce_{0.15}CuO_{4-delta}

By Cu NMR we studied the spin and charge structure in Nd_{2-x}Ce_{x}CuO_{4-delta}. For x=0.15, starting from a superconducting sample, the low temperature magnetic order in the sample reoxygenated under 1 bar oxygen at 900^0 C, reveals a peculiar modulation of the internal field, indicative for a phase characterized by large charge droplets ('Blob'-phase). By prolonged reoxygenation at 4 bar the blobs brake up and the spin structure changes to that of an ordered antiferromagnet (AF). We conclude that the superconductivity in the n-type systems competes with a genuine type I Mott-insulating state

Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with non-Hermitian potential $V$ lie in the disjoint union of two disks in the right and left half plane, respectively, provided that the $L^1-norm$ of $V$ is bounded from above by the speed of light times the reduced Planck constant. An analogous result for the Schr\"odinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on $V$ implies the absence of nonreal eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials

Ramification theory for varieties over a local field

We define generalizations of classical invariants of wild ramification for coverings on a variety of arbitrary dimension over a local field. For an l-adic sheaf, we define its Swan class as a 0-cycle class supported on the wild ramification locus. We prove a formula of Riemann-Roch type for the Swan conductor of cohomology together with its relative version, assuming that the local field is of mixed characteristic. We also prove the integrality of the Swan class for curves over a local field as a generalization of the Hasse-Arf theorem. We derive a proof of a conjecture of Serre on the Artin character for a group action with an isolated fixed point on a regular local ring, assuming the dimension is 2.Comment: 159 pages, some corrections are mad

Jack polynomials with prescribed symmetry and hole propagator of spin Calogero-Sutherland model

We study the hole propagator of the Calogero-Sutherland model with SU(2) internal symmetry. We obtain the exact expression for arbitrary non-negative integer coupling parameter $\beta$ and prove the conjecture proposed by one of the authors. Our method is based on the theory of the Jack polynomials with a prescribed symmetry.Comment: 12 pages, REVTEX, 1 eps figur

Derivation of Green's Function of Spin Calogero-Sutherland Model by Uglov's Method

Hole propagator of spin 1/2 Calogero-Sutherland model is derived using Uglov's method, which maps the exact eigenfunctions of the model, called Yangian Gelfand-Zetlin basis, to a limit of Macdonald polynomials (gl_2-Jack polynomials). To apply this mapping method to the calculation of 1-particle Green's function, we confirm that the sum of the field annihilation operator on Yangian Gelfand-Zetlin basis is transformed to the field annihilation operator on gl_2-Jack polynomials by the mapping. The resultant expression for hole propagator for finite-size system is written in terms of renormalized momenta and spin of quasi-holes and the expression in the thermodynamic limit coincides with the earlier result derived by another method. We also discuss the singularity of the spectral function for a specific coupling parameter where the hole propagator of spin Calogero-Sutherland model becomes equivalent to dynamical colour correlation function of SU(3) Haldane-Shastry model.Comment: 36 pages, 8 figure

Multipartite entanglement in quantum spin chains

We study the occurrence of multipartite entanglement in spin chains. We show that certain genuine multipartite entangled states, namely W states, can be obtained as ground states of simple XX type ferromagnetic spin chains in a transverse magnetic field, for any number of sites. Moreover, multipartite entanglement is proven to exist even at finite temperatures. A transition from a product state to a multipartite entangled state occurs when decreasing the magnetic field to a critical value. Adiabatic passage through this point can thus lead to the generation of multipartite entanglement.Comment: 4 pages, 1 figur

Transmission and Reflection of Collective Modes in Spin-1 Bose-Einstein Condensate

We study tunneling properties of collective excitations in spin-1 Bose-Einstein condensates. In the absence of magnetic fields, the total transmission in the long wavelength limit occurs in all kinds of excitations but the quadrupolar spin mode in the ferromagnetic state. The quadrupolar spin mode alone shows the total reflection. A difference between those excitations comes from whether the wavefunction of an excitation corresponds to that of the condensate in the long wavelength limit. The correspondence results in the total transmission as in the spinless BEC.Comment: 6 pages, 5 figure