Nonparametric IV estimation of shape-invariant Engel curves

This paper concerns the identification and estimation of a shape-invariant Engel curve system with endogenous total expenditure. The shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of Engel curves. Our focus is on the identification and estimation of both the nonparametric shape of the Engel curve and the parametric specification of the demographic scaling parameters. We present a new identification condition, closely related to the concept of bounded completeness in statistics. The estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions allowing for endogeneity. We establish a new root mean squared convergence rate for the nonparametric IV regression when the endogenous regressor has unbounded support. Root-n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of ‘low-level’ sufficient conditions. Monte Carlo simulations shed lights on the choice of smoothing parameters and demonstrate that the sieve IV estimator performs well. An application is made to the estimation of Engel curves using the UK Family Expenditure Survey and shows the importance of adjusting for endogeneity in terms of both the curvature and demographic parameters of systems of Engel curves

Semi-nonparametric IV estimation of shape-invariant Engel curves

This paper studies a shape-invariant Engel curve system with endogenous total expenditure, in which the shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric Engel curves. We focus on the identification and estimation of both the nonparametric shapes of the Engel curves and the parametric specification of the demographic scaling parameters. The identification condition relates to the bounded completeness and the estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions, allowing for endogeneity. We establish a new root mean squared convergence rate for the nonparametric instrumental variable regression when the endogenous regressor could have unbounded support. Root-n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of "low-level" sufficient conditions. Our empirical application using the U.K. Family Expenditure Survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of Engel curves

Quantum Topological Excitations: from the Sawtooth Lattice to the Heisenberg Chain

The recently elucidated structure of the delafossite YCuO$_{2.5}$ reveals a Cu-O network with nearly independent $\Delta$ chains having different interactions between the $s=1/2$ spins. Motivated by this result, we study the $\Delta$ chain for various ratios $J_{\rm bb}/J_{\rm bv}$ of the base-base and base-vertex interactions. By exact diagonalization and extrapolation, we show that the elementary excitation spectrum, which (within numerical error) is the same for total spins $S_{\rm tot}=0$ and 1, has a gap only in the interval $0.4874(1) \leq J_{\rm bb}/J_{\rm bv} \leq 1.53(1)$. The gap is dispersionless for $J_{\rm bb}/J_{\rm bv}=1$, but has increasing $k$-dependence as $J_{\rm bb}/J_{\rm bv}$ moves away from unity, related to the instability of dimers in the ground state.Comment: 4 pages, 6 figures (revtex twocolumn

Finite Temperature Behavior of Small Silicon and Tin Clusters: An Ab Initio Molecular Dynamics Study

The finite temperature behavior of small Silicon (Si$_{10}$, Si$_{15}$, and Si$_{20}$) and Tin (Sn$_{10}$ and Sn$_{20}$) clusters is studied using isokinetic Born-Oppenheimer molecular dynamics. The lowest equilibrium structures of all the clusters are built upon a highly stable tricapped trigonal prism unit which is seen to play a crucial role in the finite temperature behavior of these clusters. Thermodynamics of small tin clusters (Sn$_{10}$ and Sn$_{20}$) is revisited in light of the recent experiments on tin clusters of sizes 18-21 [G. A. Breaux et. al. Phys. Rev. B {\bf 71} 073410 (2005)]. We have calculated heat capacities using multiple histogram technique for Si$_{10}$, Sn$_{10}$ and Si$_{15}$ clusters. Our calculated specific heat curves have a main peak around 2300 K and 2200 K for Si$_{10}$ and Sn$_{10}$ clusters respectively. However, various other melting indicators such as root mean square bond length fluctuations, mean square displacements show that diffusive motion of atoms within the cluster begins around 650 K. The finite temperature behavior of Si$_{10}$ and Sn$_{10}$ is dominated by isomerization and it is rather difficult to discern the temperature range for transition region. On the other hand, Si$_{15}$ does show a liquid like behavior over a short temperature range followed by the fragmentation observed around 1800 K. Finite temperature behavior of Si$_{20}$ and Sn$_{20}$ show that these clusters do not melt but fragment around 1200 K and 650 K respectively.Comment: 9 figure

Field-theory calculation of the electric dipole moment of the neutron and paramagnetic atoms

Electric dipole moments (edms) of bound states that arise from the constituents having edms are studied with field-theoretic techniques. The systems treated are the neutron and a set of paramagnetic atoms. In the latter case it is well known that the atomic edm differs greatly from the electron edm when the internal electric fields of the atom are taken into account. In the nonrelativistic limit these fields lead to a complete suppression, but for heavy atoms large enhancement factors are present. A general bound-state field theory approach applicable to both the neutron and paramagnetic atoms is set up. It is applied first to the neutron, treating the quarks as moving freely in a confining spherical well. It is shown that the effect of internal electric fields is small in this case. The atomic problem is then revisited using field-theory techniques in place of the usual Hamiltonian methods, and the atomic enhancement factor is shown to be consistent with previous calculations. Possible application of bound-state techniques to other sources of the neutron edm is discussed.Comment: 21 pages, 5 figure

An analytical treatment of in-plane magnetotransport in the Falicov-Sievert model

We derive an analytical expression which allows efficient computation of the effect of all the Fermi surface trajectories induced by a combination of Bragg scattering and magnetic breakdown on the in-plane components of the resistivity tensor. The particular network of coupled orbits which we consider was first formulated by Falicov and Sievert, who studied the problem numerically. Our approach, based upon a method used previously to derive an analytical solution for interlayer transport, allows us to show that the conductivity tensor can be written as a sum of a matrix representing the effect of total magnetic breakdown and one representing a combination of complex electronic trajectories, and we find a compact expression for the in-plane components of the resistivity tensor that can be evaluated straightforwardly.Comment: 4 pages, 4 figure

The inverse-Compton ghost HDF 130 and the giant radio galaxy 6C 0905+3955: matching an analytic model for double radio source evolution

We present new GMRT observations of HDF 130, an inverse-Compton (IC) ghost of a giant radio source that is no longer being powered by jets. We compare the properties of HDF 130 with the new and important constraint of the upper limit of the radio flux density at 240 MHz to an analytic model. We learn what values of physical parameters in the model for the dynamics and evolution of the radio luminosity and X-ray luminosity (due to IC scattering of the cosmic microwave background (CMB)) of a Fanaroff-Riley II (FR II) source are able to describe a source with features (lobe length, axial ratio, X-ray luminosity, photon index and upper limit of radio luminosity) similar to the observations. HDF 130 is found to agree with the interpretation that it is an IC ghost of a powerful double-lobed radio source, and we are observing it at least a few Myr after jet activity (which lasted 5--100 Myr) has ceased. The minimum Lorentz factor of injected particles into the lobes from the hotspot is preferred to be $\gamma\sim10^3$ for the model to describe the observed quantities well, assuming that the magnetic energy density, electron energy density, and lobe pressure at time of injection into the lobe are linked by constant factors according to a minimum energy argument, so that the minimum Lorentz factor is constrained by the lobe pressure. We also apply the model to match the features of 6C 0905+3955, a classical double FR II galaxy thought to have a low-energy cutoff of $\gamma\sim10^4$ in the hotspot due to a lack of hotspot inverse-Compton X-ray emission. The models suggest that the low-energy cutoff in the hotspots of 6C 0905+3955 is $\gamma\gtrsim 10^3$, just slightly above the particles required for X-ray emission.Comment: 9 pages, 3 figure