Studies of Vibrational Properties in Ga Stabilized d-Pu by Extended X-ray Absorption Fine Structure

Temperature dependent extended x-ray absorption fine structure (EXAFS) spectra were measured for a 3.3 at% Ga stabilized Pu alloy over the range T= 20 - 300 K at both the Ga K-edge and the Pu L_III-edge. The temperature dependence of the pair-distance distribution widths, \sigma(T) was accurately modeled using a correlated-Debye model for the lattice vibrational properties, suggesting Debye-like behavior in this material. We obtain pair- specific correlated-Debye temperatures, \Theta_cD, of 110.7 +/- 1.7 K and 202.6 +/- 3.7 K, for the Pu-Pu and Ga-Pu pairs, respectively. These results represent the first unambiguous determination of Ga-specific vibrational properties in PuGa alloys, and indicate the Ga-Pu bonds are significantly stronger than the Pu-Pu bonds. This effect has important implications for lattice stabilization mechanisms in these alloys.Comment: 7 pages, 4 figures, Phys. Rev. B in pres

Induced subgraphs in sparse random graphs with given degree sequence

For any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is a given graph $H$ on the vertex set $S$. The result holds for any $d=o(n^{1/3})$ and is further extended to $\mathcal{G}_{{\bf d}}$, the probability space of random graphs with a given degree sequence $\bf d$.Comment: 31 pages, 11 figure

Canonical Expansion of PT-Symmetric Operators and Perturbation Theory

Let $H$ be any \PT symmetric Schr\"odinger operator of the type $-\hbar^2\Delta+(x_1^2+...+x_d^2)+igW(x_1,...,x_d)$ on $L^2(\R^d)$, where $W$ is any odd homogeneous polynomial and $g\in\R$. It is proved that $\P H$ is self-adjoint and that its eigenvalues coincide (up to a sign) with the singular values of $H$, i.e. the eigenvalues of $\sqrt{H^\ast H}$. Moreover we explicitly construct the canonical expansion of $H$ and determine the singular values $\mu_j$ of $H$ through the Borel summability of their divergent perturbation theory. The singular values yield estimates of the location of the eigenvalues \l_j of $H$ by Weyl's inequalities.Comment: 20 page

Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity

This paper is concerned with the inhomogeneous nonlinear Shrödinger equation (INLS-equation)iu_t + Δu + V(Єx)│u│^pu = 0, x Є R^N. In the critical and supercritical cases p ≥ 4/N, with N ≥ 2, it is shown here that standing-wave solutions of (INLS-equation) on H^1(R^N) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the potential term V with a small Є > 0

Irrotational dust with Div H=0

For irrotational dust the shear tensor is consistently diagonalizable with its covariant time derivative: $\sigma_{ab}=0=\dot{\sigma}_{ab},\; a\neq b$, if and only if the divergence of the magnetic part of the Weyl tensor vanishes: $div~H = 0$. We show here that in that case, the consistency of the Ricci constraints requires that the magnetic part of the Weyl tensor itself vanishes: $H_{ab}=0$.Comment: 19 pages. Latex. Also avaliable at http://shiva.mth.uct.ac.za/preprints/text/lesame2.te

Strong Enhancement of Superconducting Correlation in a Two-Component Fermion Gas

We study high-density electron-hole (e-h) systems with the electron density slightly larger than the hole density. We find a new superconducting phase, in which the excess electrons form Cooper pairs moving in an e-h BCS phase. The coexistence of the e-h and e-e orders is possible because e and h have opposite charges, whereas analogous phases are impossible in the case of two fermion species that have the same charge or are neutral. Most strikingly, the e-h order enhances the superconducting e-h order parameter by more than one order of magnitude as compared with that given by the BCS formula, for the same value of the effective e-e attractive potential \lambda^{ee}. This new phase should be observable in an e-h system created by photoexcitation in doped semiconductors at low temperatures.Comment: 5 pages including 5 PostScript figure

A new non-arithmetic lattice in PU(3,1)

We study the arithmeticity of the Couwenberg-Heckman-Looijenga lattices in PU(n,1), and show that they contain a non-arithmetic lattice in PU(3,1) which is not commensurable to the non-arithmetic Deligne-Mostow lattice in PU(3,1)