Extension of random-phase approximation preserving energy weighted sum rules: an application to a 3-level Lipkin model

A limitation common to all extensions of random-phase approximation including only particle-hole configurations is that they violate to some extent the energy weighted sum rules. Considering one such extension, the improved RPA (IRPA), already used to study the electronic properties of metallic clusters, we show how it can be generalized in order to eliminate this drawback. This is achieved by enlarging the configuration space, including also elementary excitations corresponding to the annihilation of a particle (hole) and the creation of another particle (hole) on the correlated ground state. The approach is tested within a solvable 3-level model.Comment: 2 figure

Good methods for coping with missing data in decision trees

We propose a simple and effective method for dealing with missing data in decision trees used for classification. We call this approach 'missingness incorporated in attributes' (MIA). It is very closely related to the technique of treating 'missing' as a category in its own right, generalizing it for use with continuous as well as categorical variables. We show through a substantial data-based study of classification accuracy that MIA exhibits consistently good performance across a broad range of data types and of sources and amounts of missingness. It is competitive with the best of the rest (particularly, a multiple imputation EM algorithm method; EMMI) while being conceptually and computationally simpler. A simple combination of MIA and EMMI is slower but even more accurate

Nuclear and nucleon transitions of the H di-baryon

We consider 3 types of processes pertinent to the phenomenology of an H di-baryon: conversion of two $\Lambda$'s in a doubly-strange hypernucleus to an H, decay of the H to two baryons, and -- if the H is light enough -- conversion of two nucleons in a nucleus to an H. We compute the spatial wavefunction overlap using the Isgur-Karl and Bethe-Goldstone wavefunctions, and treat the weak interactions phenomenologically. The observation of $\Lambda$ decays from doubly-strange hypernuclei puts a constraint on the H wavefunction which is plausibly satisfied. In this case the H is very long-lived as we calculate. An absolutely stable H is not excluded at present. SuperK can provide valuable limits

Detecting local synchronization in coupled chaotic systems

We introduce a technique to detect and quantify local functional dependencies between coupled chaotic systems. The method estimates the fraction of locally syncronized configurations, in a pair of signals with an arbitrary state of global syncronization. Application to a pair of interacting Rossler oscillators shows that our method is capable to quantify the number of dynamical configurations where a local prediction task is possible, also in absence of global synchronization features

Fully-Renormalized QRPA fulfills Ikeda sum rule exactly

The renormalized quasiparticle-RPA is reformulated for even-even nuclei using restrictions imposed by the commutativity of the phonon creation operator with the total particle number operator. This new version, Fully-Renormalized QRPA (FR-QRPA), is free from the spurious low-energy solutions. Analytical proof is given that the Ikeda sum rule is fullfiled within the FR-QRPA.Comment: 9 page

Magnetic catalysis and anisotropic confinement in QCD

The expressions for dynamical masses of quarks in the chiral limit in QCD in a strong magnetic field are obtained. A low energy effective action for the corresponding Nambu-Goldstone bosons is derived and the values of their decay constants as well as the velocities are calculated. The existence of a threshold value of the number of colors $N^{thr}_c$, dividing the theories with essentially different dynamics, is established. For the number of colors $N_c \ll N^{thr}_c$, an anisotropic dynamics of confinement with the confinement scale much less than $\Lambda_{QCD}$ and a rich spectrum of light glueballs is realized. For $N_c$ of order $N^{thr}_c$ or larger, a conventional confinement dynamics takes place. It is found that the threshold value $N^{thr}_c$ grows rapidly with the magnetic field [$N^{thr}_c \gtrsim 100$ for $|eB| \gtrsim (1{GeV})^2$]. In contrast to QCD with a nonzero baryon density, there are no principal obstacles for checking these results and predictions in lattice computer simulations.Comment: 10 pages, 1 figure. REVTeX. Minor correction. To appear in Phys. Rev.

Large N_c, chiral approach to M_eta' at finite temperature

We study the temperature dependence of the eta and eta' meson masses within the framework of U(3)_L x U(3)_R chiral perturbation theory, up to next-to-leading order in a simultaneous expansion in momenta, quark masses and number of colours. We find that both masses decrease at low temperatures, but only very slightly. We analyze higher order corrections and argue that large N_c suggests a discontinuous drop of M_eta' at the critical temperature of deconfinement T_c, consistent with a first order transition to a phase with approximate U(1)_A symmetry.Comment: 21 pages, 6 figures. 2 footnotes added, 1 reference changed and 1 typo corrected. To be published in Phys. Rev.

Relative spins and excitation energies of superdeformed bands in 190Hg: Further evidence for octupole vibration

An experiment using the Eurogam Phase II gamma-ray spectrometer confirms the existence of an excited superdeformed (SD) band in 190Hg and its very unusual decay into the lowest SD band over 3-4 transitions. The energies and dipole character of the transitions linking the two SD bands have been firmly established. Comparisons with RPA calculations indicate that the excited SD band can be interpreted as an octupole-vibrational structure.Comment: 12 pages, latex, 4 figures available via WWW at http://www.phy.anl.gov/bgo/bc/hg190_nucl_ex.htm

Propagators in Noncommutative Instantons

We explicitly construct Green functions for a field in an arbitrary representation of gauge group propagating in noncommutative instanton backgrounds based on the ADHM construction. The propagators for spinor and vector fields can be constructed in terms of those for the scalar field in noncommutative instanton background. We show that the propagators in the adjoint representation are deformed by noncommutativity while those in the fundamental representation have exactly the same form as the commutative case.Comment: 28 pages, Latex, v2: A few typos correcte

The check of QCD based on the tau-decay data analysis in the complex q^2-plane

The thorough analysis of the ALEPH data on hadronic tau-decay is performed in the framework of QCD. The perturbative calculations are performed in 3 and 4-loop approximations. The terms of the operator product expansion (OPE) are accounted up to dimension D=8. The value of the QCD coupling constant alpha_s(m_tau^2)=0.355 pm 0.025 was found from hadronic branching ratio R_tau. The V+A and V spectral function are analyzed using analytical properties of polarization operators in the whole complex q^2-plane. Borel sum rules in the complex q^2 plane along the rays, starting from the origin, are used. It was demonstrated that QCD with OPE terms is in agreement with the data for the coupling constant close to the lower error edge alpha_s(m_tau^2)=0.330. The restriction on the value of the gluonic condensate was found =0.006 pm 0.012 GeV^2. The analytical perturbative QCD was compared with the data. It is demonstrated to be in strong contradiction with experiment. The restrictions on the renormalon contribution were found. The instanton contributions to the polarization operator are analyzed in various sum rules. In Borel transformation they appear to be small, but not in spectral moments sum rules.Comment: 24 pages; 1 latex + 13 figure files. V2: misprints are corrected, uncertainty in alpha_s is explained in more transparent way, acknowledgement is adde