Supersymmetric quantum mechanics and the Korteweg-de Vries hierarchy

The connection between supersymmetric quantum mechanics and the Korteweg- de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the $\tau$-function by means of supersymmetric quantum mechanics is discussed.Comment: 16 pages, latex, EFI 93/2

Formation of standing shocks in stellar winds and related astrophysical flows

Stellar winds and other analogous astrophysical flows can be described, to lowest order, by the familiar one dimensional hydrodynamic equations which, being nonlinear, admit in some instances discontinuous as well as continuous transonic solutions for identical inner boundary conditions. The characteristics of the time dependent differential equations of motion are described to show how a perturbation changes profile in time and, under well defined conditions, develops into a stationary shock discontinuity. The formation of standing shocks in wind type astrophysical flows depends on the fulfillment of appropriate necessary conditions, which are determined by the conservation of mass, momentum and energy across the discontinuity, and certain sufficient conditions, which are determined by the flow's history

Recent Results in Bottomonium

Great strides have been made in the understanding of bound states of a bottom quark $b$ and its antiquark $\bar b$ since the discovery of the first $\Upsilon$ resonances in 1977. These {\it bottomonium} bound states have a rich spectrum whose masses and transition amplitudes shed valuable light on the strong interactions. The present article reviews some recent developments in bottomonium physics. These include the discovery of the spin-singlet states $\eta_b$ and $h_b$, the first D-wave states, one or more candidates for spin-triplet $\chi_b(3P)$ excitations, and above-threshold states with strong transitions to states below threshold. Information on transitions, production, and signatures of new physics is also presented.Comment: 47 pages, 2 figures, to be submitted to Annual Review of Nuclear and Particle Scienc

Electroweak Constraints from Atomic Parity Violation and Neutrino Scattering

Precision electroweak physics can provide fertile ground for uncovering new physics beyond the Standard Model (SM). One area in which new physics can appear is in so-called "oblique corrections", i.e., next-to-leading order expansions of bosonic propagators corresponding to vacuum polarization. One may parametrize their effects in terms of quantities $S$ and $T$ that discriminate between conservation and non-conservation of isospin. This provides a means of comparing the relative contributions of precision electroweak experiments to constraints on new physics. Given the prevalence of strongly $T$-sensitive experiments, there is an acute need for further constraints on $S$, such as provided by atomic parity-violating experiments on heavy atoms. We evaluate constraints on $S$ arising from recently improved calculations in the Cs atom. We show that the top quark mass $m_t$ provides stringent constraints on $S$ within the context of the Standard Model. We also consider the potential contributions of next-generation neutrino scattering experiments to improved $(S,T)$ constraints.Comment: 10 pages, 4 figures, final corrected version to be published in Physical Review

Nax_xCoO2_2 in the x -> 0 Regime: Coupling of Structure and Correlation effects

The study of the strength of correlations in Na$_x$CoO$_2$ is extended to the x=0 end of the phase diagram where Mott insulating behavior has been widely anticipated. Inclusion of correlation as modeled by the LDA+U approach leads to a Mott transition in the $a_g$ subband if U is no less than U$_c$=2.5 eV. Thus U smaller than U$_c$ is required to model the metallic, nonmagnetic CoO$_2$ compound reported by Tarascon and coworkers. The orbital-selective Mott transition of the $a_g$ state, which is essentially degenerate with the $e'_{g}$ states, occurs because of the slightly wider bandwidth of the $a_g$ bands. The metal-insulator transition is found to be strongly coupled to the Co-O bond length, due to associated changes in the $t_{2g}$ bandwidth, but the largest effects occur only at a reduced oxygen height that lies below the equilibrium position.Comment: 8 pages with 9 embedded figure

On the electronic structure of CaCuO2 and SrCuO2

Recent electronic structure calculations for the prototypical lowdimensional cuprate compounds CaCuO2 ans SrCuO2 performed by Wu et. al. (J. Phys.: Condens. Matter v. 11 p.4637 (1999))are critically reconsidered, applying high precision full-potential bandstructure methods. It is shown that the bandstructure calculations presented by the authors contain several important inconsistencies, which make their main conclusions highly questionable.Comment: 4 pages, 3 figures, submitted to J. Phys. Condens. Matte