The smallest eigenvalue of Hankel matrices

Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive measure with moments of any order. We study the large N behaviour of the smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of lambda_N can be arbitrarily slow or arbitrarily fast. In the indeterminate case, where lambda_N is known to be bounded below by a positive constant, we prove that the limit of the n'th smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity with n. The special case of the Stieltjes-Wigert polynomials is discussed

On a Cahn--Hilliard--Darcy system for tumour growth with solution dependent source terms

We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic reaction-diffusion equation. The Darcy law gives rise to an elliptic equation for the pressure that is coupled to the convective Cahn--Hilliard equation through convective and source terms. Both Dirichlet and Robin boundary conditions are considered for the pressure variable, which allows for the source terms to be dependent on the solution variables.Comment: 18 pages, changed proof from fixed point argument to Galerkin approximatio

Influence of gauge-field fluctuations on composite fermions near the half-filled state

Taking into account the transverse gauge field fluctuations, which interact with composite fermions, we examine the finite temperature compressibility of the fermions as a function of an effective magnetic field $\Delta B = B - 2 n_e hc/e$ ($n_e$ is the density of electrons) near the half-filled state. It is shown that, after including the lowest order gauge field correction, the compressibility goes as ${\partial n \over \partial \mu} \propto e^{- \Delta \omega_c / 2 T} \left ( 1 + {A (\eta) \over \eta - 1} {(\Delta \omega_c)^{2 \over 1 + \eta} \over T} \right )$ for $T \ll \Delta \omega_c$, where $\Delta \omega_c = {e \Delta B \over mc}$. Here we assume that the interaction between the fermions is given by $v ({\bf q}) = V_0 / q^{2 - \eta} \ (1 \le \eta \le 2)$, where $A (\eta)$ is a $\eta$ dependent constant. This result can be interpreted as a divergent correction to the activation energy gap and is consistent with the divergent renormalization of the effective mass of the composite fermions.Comment: Plain Tex, 24 pages, 5 figures available upon reques

Nonvanishing Local Moment in Triplet Superconductors

The Kondo effect in a $p_x + {\rm i} p_y$-wave superconductor is studied by applying the Wilson's numerical renormalization group method. In this type of superconductor with a full energy gap like a s-wave one, the ground state is always a spin doublet, while a local spin is shrunk by the Kondo effect. The calculated magnetic susceptibility indicates that the spin of the ground state is generated by the orbital effect of the $p_x + {\rm i} p_y$-wave Cooper pairs. The effect of spin polarization of the triplet superconductor is also discussed.Comment: 5 pages, 4 figures, to be published in J. Phys. Soc. Jp

Polyurea-Functionalized Multiwalled Carbon Nanotubes

An in situ polycondensation approach was applied to functionalize multiwalled carbon nanotubes (MWNTs), resulting in various linear or hyperbranched polycondensed polymers [e.g., polyureas, polyurethanes, and poly(urea-urethane)-bonded carbon nanotubes]. The quantity of the grafted polymer can be easily controlled by the feed ratio of monomers. As a typical example, the polyurea-functionalized MWNTs were measured and characterized in detail. The oxidized MWNTs (MWNT-COOH) were converted into acyl chloride-functionalized MWNTs (MWNT-COCl) by reaction with neat thionyl chloride (SOCl2). MWNT-COCl was reacted with excess 1,6-diaminohexane, affording amino-functionalized MWNTs (MWNT-NH2). In the presence of MWNT-NH2, the polyurea was covalently coated onto the surfaces of the nanotube by in situ polycondensation of diisocyanate [e.g., 4,4‘-methylenebis(phenylisocyanate)] and 1,6-diaminohexane, followed by the removal of free polymer via repeated filtering and solvent washing. The coated polyurea content can be controlled to some extent by adjusting the feed ratio of the isocyanato and amino groups. The structure and morphology of the resulting nanocomposites were characterized by FTIR, NMR, Raman, confocal Raman, TEM, EDS, and SEM measurements. The polyurea-coated MWNTs showed interesting self-assembled flat- or flowerlike morphologies in the solid state. The signals corresponding to that of the D and G bands of the carbon nanotubes were strongly attenuated after polyurea was chemically tethered to the MWNT surfaces. Comparative experiments showed that the grafted polymer species and structures have a strong effect on the Raman signals of polymer-functionalized MWNTs

Wolfram Syndrome protein, Miner1, regulates sulphydryl redox status, the unfolded protein response, and Ca2+ homeostasis.

Miner1 is a redox-active 2Fe2S cluster protein. Mutations in Miner1 result in Wolfram Syndrome, a metabolic disease associated with diabetes, blindness, deafness, and a shortened lifespan. Embryonic fibroblasts from Miner1(-/-) mice displayed ER stress and showed hallmarks of the unfolded protein response. In addition, loss of Miner1 caused a depletion of ER Ca(2+) stores, a dramatic increase in mitochondrial Ca(2+) load, increased reactive oxygen and nitrogen species, an increase in the GSSG/GSH and NAD(+)/NADH ratios, and an increase in the ADP/ATP ratio consistent with enhanced ATP utilization. Furthermore, mitochondria in fibroblasts lacking Miner1 displayed ultrastructural alterations, such as increased cristae density and punctate morphology, and an increase in O2 consumption. Treatment with the sulphydryl anti-oxidant N-acetylcysteine reversed the abnormalities in the Miner1 deficient cells, suggesting that sulphydryl reducing agents should be explored as a treatment for this rare genetic disease

Experimental demonstration of a BDCZ quantum repeater node

Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication (of the order of 100 km) has been achieved; however, serious problems occur beyond this distance scale, mainly due to inevitable photon loss in the transmission channel. Quantum communication eventually fails when the probability of a dark count in the photon detectors becomes comparable to the probability that a photon is correctly detected. To overcome this problem, Briegel, D\"{u}r, Cirac and Zoller (BDCZ) introduced the concept of quantum repeaters, combining entanglement swapping and quantum memory to efficiently extend the achievable distances. Although entanglement swapping has been experimentally demonstrated, the implementation of BDCZ quantum repeaters has proved challenging owing to the difficulty of integrating a quantum memory. Here we realize entanglement swapping with storage and retrieval of light, a building block of the BDCZ quantum repeater. We follow a scheme that incorporates the strategy of BDCZ with atomic quantum memories. Two atomic ensembles, each originally entangled with a single emitted photon, are projected into an entangled state by performing a joint Bell state measurement on the two single photons after they have passed through a 300-m fibre-based communication channel. The entanglement is stored in the atomic ensembles and later verified by converting the atomic excitations into photons. Our method is intrinsically phase insensitive and establishes the essential element needed to realize quantum repeaters with stationary atomic qubits as quantum memories and flying photonic qubits as quantum messengers.Comment: 5 pages, 4 figure

The Energy Density in the Maxwell-Chern-Simons Theory

A two-dimensional nonrelativistic fermion system coupled to both electromagnetic gauge fields and Chern-Simons gauge fields is analysed. Polarization tensors relevant in the quantum Hall effect and anyon superconductivity are obtained as simple closed integrals and are evaluated numerically for all momenta and frequencies. The correction to the energy density is evaluated in the random phase approximation (RPA), by summing an infinite series of ring diagrams. It is found that the correction has significant dependence on the particle number density. In the context of anyon superconductivity, the energy density relative to the mean field value is minimized at a hole concentration per lattice plaquette (0.05 \sim 0.06) (p_c a/\hbar)^2 where p_c and a are the momentum cutoff and lattice constant, respectively. At the minimum the correction is about -5 % \sim -25 %, depending on the ratio (2m \omega_c)/(p_c^2) where \omega_c is the frequency cutoff. In the Jain-Fradkin-Lopez picture of the fractional quantum Hall effect the RPA correction to the energy density is very large. It diverges logarithmically as the cutoff is removed, implying that corrections beyond RPA become important at large momentum and frequency.Comment: 19 pages (plain Tex), 12 figures not included, UMN-TH-1246/9

Finite-Wavevector Electromagnetic Response of Fractional Quantized Hall States

A fractional quantized Hall state with filling fraction $\nu = p/(2mp+1)$ can be modeled as an integer quantized Hall state of transformed fermions, interacting with a Chern-Simons field. The electromagnetic response function for these states at arbitrary frequency and wavevector can be calculated using a semiclassical approximation or the Random Phase Approximation (RPA). However, such calculations do not properly take into account the large effective mass renormalization which is present in the Chern-Simons theory. We show how the mass renormalization can be incorporated in a calculation of the response function within a Landau Fermi liquid theory approach such that Kohn's theorem and the $f$-sum rules are properly satisfied. We present results of such calculations.Comment: 19 pages (REVTeX 3.0), 5 figures available on request; HU-CMT-93S0

The nature and role of trap states in a dendrimer-based organic field-effect transistor explosive sensor

We report the fabrication and charge transport characterization of carbazole dendrimer-based organic field-effect transistors (OFETs) for the sensing of explosive vapors. After exposure to para-nitrotoluene (pNT) vapor, the OFET channel carrier mobility decreases due to trapping induced by the absorbed pNT. The influence of trap states on transport in devices before and after exposure to pNT vapor has been determined using temperature-dependent measurements of the field-effect mobility. These data clearly show that the absorption of pNT vapor into the dendrimer active layer results in the formation of additional trap states. Such states inhibit charge transport by decreasing the density of conducting states. (C) 2013 AIP Publishing LLC