Big q-Laguerre and q-Meixner polynomials and representations of the algebra U_q(su(1,1))

Diagonalization of a certain operator in irreducible representations of the positive discrete series of the quantum algebra U_q(su(1,1)) is studied. Spectrum and eigenfunctions of this operator are found in an explicit form. These eigenfunctions, when normalized, constitute an orthonormal basis in the representation space. The initial U_q(su(1,1))-basis and the basis of eigenfunctions are interrelated by a matrix with entries, expressed in terms of big q-Laguerre polynomials. The unitarity of this connection matrix leads to an orthogonal system of functions, which are dual with respect to big q-Laguerre polynomials. This system of functions consists of two separate sets of functions, which can be expressed in terms of q-Meixner polynomials M_n(x;b,c;q) either with positive or negative values of the parameter b. The orthogonality property of these two sets of functions follows directly from the unitarity of the connection matrix. As a consequence, one obtains an orthogonality relation for q-Meixner polynomials M_n(x;b,c;q) with b<0. A biorthogonal system of functions (with respect to the scalar product in the representation space) is also derived.Comment: 15 pages, LaTe

Tracing Galaxy Assembly: Tadpole Galaxies in the Hubble Ultra Deep Field

In the Hubble Ultra Deep Field (HUDF) an abundance of galaxies is seen with a knot at one end plus an extended tail, resembling a tadpole. These "tadpole galaxies" appear dynamically unrelaxed--presumably in an early merging state--where tidal interactions likely created the distorted knot-plus-tail morphology. Here we systematically select tadpole galaxies from the HUDF and study their properties as a function of their photometric redshifts. In a companion HUDF variability study, Cohen et al. (2005) revealed a total of 45 variable objects believed to be Active Galactic Nuclei (AGN). Here we show that this faint AGN sample has no overlap with the tadpole galaxy sample, as predicted by theoretical work. The tadpole morphology--combined with the lack of overlap with the variable objects--supports the idea that these galaxies are in the process of an early-stage merger event, i.e., at a stage that likely precedes the "turn-on" of any AGN component and the onset of any point-source variability.Comment: 7 pages, 4 figures. Accepted for publication by Astrophysical Journa

On the polarization properties of the charmed baryon Lambda^+_c in the Lambda^+_c -> p + K^- + pi^+ + pi^0 decay

The polarization properties of the charmed Lambda^+_c baryon are investigated in weak non-leptonic four-body Lambda^+_c -> p + K^- + pi^+ + pi^0 decay. The probability of this decay and the angular distribution of the probability are calculated in the effective quark model with chiral U(3)XU(3) symmetry incorporating Heavy Quark Effective theory (HQET) and the extended Nambu-Jona-Lasinio model with a linear realization of chiral U(3)XU(3) symmetry. The theoretical value of the probability of the decay Lambda^+_c -> p + K^- + pi^+ + pi^0 relative to the probability of the decay Lambda^+_c -> p + K^- + pi^+ does not contain free parameters and fits well experimental data. The application of the obtained results to the analysis of the polarization of the Lambda^+_c produced in the processes of photo and hadroproduction is discussed.Comment: 10 pages, no figures, Late

Superconductivity in iron silicide Lu2Fe3Si5 probed by radiation-induced disordering

Resistivity r(T), Hall coefficient RH(T), superconducting temperature Tc, and the slope of the upper critical field -dHc2/dT were studied in poly- and single-crystalline samples of the Fe-based superconductor Lu2Fe3Si5 irradiated by fast neutrons. Atomic disordering induced by the neutron irradiation leads to a fast suppression of Tc similarly to the case of doping of Lu2Fe3Si5 with magnetic (Dy) and non-magnetic (Sc, Y) impurities. The same effect was observed in a novel FeAs-based superconductor La(O-F)FeAs after irradiation. Such behavior is accounted for by strong pair breaking that is traceable to scattering at non-magnetic impurities or radiation defects in unconventional superconductors. In such superconductors the sign of the order parameter changes between the different Fermi sheets (s+- model). Some relations that are specified for the properties of the normal and superconducting states in high-temperature superconductors are also observed in Lu2Fe3Si5. The first is the relationship -dHc2/dT ~ Tc, instead of the one expected for dirty superconductors -dHc2/dT ~ r0. The second is a correlation between the low-temperature linear coefficient a in the resistivity r = r0 + a1T, which appears presumably due to the scattering at magnetic fluctuations, and Tc; this correlation being an evidence of a tight relation between the superconductivity and magnetism. The data point to an unconventional (non-fononic) mechanism of superconductivity in Lu2Fe3Si5, and, probably, in some other Fe-based compounds, which can be fruitfully studied via the radiation-induced disordering.Comment: 7 pages, 8 figure

Topological Quantum Computing with Only One Mobile Quasiparticle

In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In this paper we show that any such quantum computation that can be done by braiding $n$ identical quasiparticles can also be done by moving a single quasiparticle around n-1 other identical quasiparticles whose positions remain fixed.Comment: 4 pages, 5 figure

Doping - dependent superconducting gap anisotropy in the two-dimensional 10-3-8 pnictide Ca10_{10}(Pt3_3As8_8)[(Fe1−x_{1-x}Ptx_{x})2_2As2_2]5_5

The characteristic features of Ca$_{10}$(Pt$_3$As$_8$)[(Fe$_{1-x}$Pt$_x$)$_2$As$_2$]$_5$ ("10-3-8") superconductor are relatively high anisotropy and a clear separation of superconductivity and structural/magnetic transitions, which allows studying the superconducting gap without complications due to the coexisting order parameters. The London penetration depth, measured in underdoped single crystals of 10-3-8 ($x =$ 0.028, 0.041, 0.042, and 0.097), shows behavior remarkably similar to other Fe-based superconductors, exhibiting robust power-law, $\Delta \lambda(T) = A T^n$. The exponent $n$ decreases from 2.36 ($x =$ 0.097, close to optimal doping) to 1.7 ($x =$ 0.028, a heavily underdoped composition), suggesting that the superconducting gap becomes more anisotropic at the dome edge. A similar trend is found in low-anisotropy superconductors based on BaFe$_2$As$_2$ ("122"), implying that it is an intrinsic property of superconductivity in iron pnictides, unrelated to the coexistence of magnetic order and superconductivity or the anisotropy of the normal state. Overall this doping dependence is consistent with $s_{\pm}$ pairing competing with intra-band repulsion

Quintom model with O(NN) symmetry

We investigate the quintom model of dark energy in the generalized case where the corresponding canonical and phantom fields possess O($N$) symmetries. Assuming exponential potentials we find that this O$(N)$ quintom paradigm exhibits novel properties comparing to the simple canonical and phantom scenarios. In particular, we find that the universe cannot result in a quintessence-type solution with $w>-1$, even in the cases where the phantom field seems to be irrelevant. On the contrary, there are always late-time attractors which correspond to accelerating universes with $w<-1$ and with a recent crossing of the phantom divide, and for a very large area of the parameter space they are the only ones. This is in contrast with the previous simple-quintom results, where an accelerating universe is a possible late-time stable solution but it is not guaranteed.Comment: 13 pages, no figur

Emergence of Oscillons in an Expanding Background

We consider a (1+1) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now lose energy, but at a rate that is exponentially small when the expansion rate is slow. We also show numerically that a universe that starts with (almost) thermal initial conditions will cool to a final state where a significant fraction of the energy of the universe -- on the order of 50% -- is stored in oscillons. If this phenomenon persists in realistic models, oscillons may have cosmological consequences.Comment: 13 pages, 4 .eps figures, uses RevTeX4; v2: clarified details of expansion, added reference

Shear Effects in Non-Homogeneous Turbulence

Motivated by recent experimental and numerical results, a simple unifying picture of intermittency in turbulent shear flows is suggested. Integral Structure Functions (ISF), taking into account explicitly the shear intensity, are introduced on phenomenological grounds. ISF can exhibit a universal scaling behavior, independent of the shear intensity. This picture is in satisfactory agreement with both experimental and numerical data. Possible extension to convective turbulence and implication on closure conditions for Large-Eddy Simulation of non-homogeneous flows are briefly discussed.Comment: 4 pages, 5 figure