Research in the general area of non-linear dynamical systems Final report, 8 Jun. 1965 - 8 Jun. 1967

Nonlinear dynamical systems research on systems stability, invariance principles, Liapunov functions, and Volterra and functional integral equation

Theory of the "honeycomb chain-channel" reconstruction of Si(111)3x1

First-principles electronic-structure methods are used to study a structural model for Ag/Si(111)3x1 recently proposed on the basis of transmission electron diffraction data. The fully relaxed geometry for this model is far more energetically favorable than any previously proposed, partly due to the unusual formation of a Si double bond in the surface layer. The calculated electronic properties of this model are in complete agreement with data from angle-resolved photoemission and scanning tunneling microscopy.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett (the ugly postscript error on page 4 has now been repaired

Scattering of positrons and electrons by alkali atoms

Absolute total scattering cross sections (Q sub T's) were measured for positrons and electrons colliding with sodium, potassium, and rubidium in the 1 to 102 eV range, using the same apparatus and experimental approach (a beam transmission technique) for both projectiles. The present results for positron-sodium and -rubidium collisions represent the first Q sub T measurements reported for these collision systems. Features which distinguish the present comparisons between positron- and electron-alkali atom Q sub T's from those for other atoms and molecules (room-temperature gases) which have been used as targets for positrons and electrons are the proximity of the corresponding positron- and electron-alkali atom Q sub T's over the entire energy range of overlap, with an indication of a merging or near-merging of the corresponding positron and electron Q sub T's near (and above) the relatively low energy of about 40 eV, and a general tendency for the positron-alkali atom Q sub T's to be higher than the corresponding electron values as the projectile energy is decreased below about 40 eV

EM Decay of X(3872) as the 11D2(2−+)1{^1D_2}(2^{-+}) charmonium

The recently BaBar results raise the possibility that X(3872) has negative parity. This makes people reconsider assigning X(3872) to the $1{^1D_2}(c\bar c)$ state. In this paper we give a general form of the wave function of $2^{-+}$ mesons. By solving the instantaneous Bethe-Salpeter equation, we get the mass spectrum and corresponding wave functions. We calculate electromagnetic decay widths of the first $2^{-+}$ state which we assume to be the X(3872) particle. The results are $\Gamma(2^{-+}(3872)\rightarrow J/\psi\gamma) = 1.59^{+0.53}_{-0.42}$ keV, $\Gamma(2^{-+}(3872)\rightarrow \psi(2S)\gamma) = 2.87^{+1.46}_{-0.97}$ eV and $\Gamma(2^{-+}(3872)\rightarrow \psi(3770)\gamma) = 0.135^{+0.066}_{-0.047}$ keV. The ratio of branch fractions of the second and first channel is about 0.002, which is inconsistent with the experimental value $3.4\pm 1.4$. So X(3872) is unlikely to be a $2^{-+}$ charmonium state. In addition, we obtain a relatively large decay width for $2^{-+}(3872)\rightarrow h_c\gamma$ channel which is $392^{+62}_{-111}$ keV.Comment: Revised versio

Bragg spectroscopy of a superfluid Bose-Hubbard gas

Bragg spectroscopy is used to measure excitations of a trapped, quantum-degenerate gas of 87Rb atoms in a 3-dimensional optical lattice. The measurements are carried out over a range of optical lattice depths in the superfluid phase of the Bose-Hubbard model. For fixed wavevector, the resonant frequency of the excitation is found to decrease with increasing lattice depth. A numerical calculation of the resonant frequencies based on Bogoliubov theory shows a less steep rate of decrease than the measurements.Comment: 11 pages, 4 figure

Symplectic embedding and Hamilton-Jacobi analysis of Proca model

Following the symplectic approach we show how to embed the Abelian Proca model into a first-class system by extending the configuration space to include an additional pair of scalar fields, and compare it with the improved Dirac scheme. We obtain in this way the desired Wess-Zumino and gauge fixing terms of BRST invariant Lagrangian. Furthermore, the integrability properties of the second-class system described by the Abelian Proca model are investigated using the Hamilton-Jacobi formalism, where we construct the closed Lie algebra by introducing operators associated with the generalized Poisson brackets.Comment: 24 page