Search for rare leptonic B decays at the Tevatron

Results of a search for the Flavor-Changing Neutral Current decay $B^0_{s,d} \to \mu^+ \mu^-$ using $p\bar{p}$ collision data at $\sqrt{s}=1.96$ TeV collected at Fermilab Tevatron collider by the CDF and D{\O}detectors are presented. CDF reports upper limits on ${\cal B} (B^0_{s} \to \mu^+ \mu^-) \leq 7.5 \cdot10^{-7}$ and ${\cal B}(B^0_{d} \to \mu^+ \mu^-) \leq 1.9 \cdot10^{-7}$ at the 95% C.L. using 171 pb$^{-1}$. The D{\O}Collaboration used 240 pb$^{-1}$ to set an even more stringent limit on the branching ratio for $B^0_{s} \to \mu^+ \mu^-$ of $5.0\cdot 10^{-7}$ at the 95% C.L.Comment: 5 pages, 2 figures, submitted to DPF 2004 conference proceedings, UC Riverside, C

Microstrip antenna array with parasitic elements

Discussed is the design of a large microstrip antenna array in terms of subarrays consisting of one fed patch and several parasitic patches. The potential advantages of this design are discussed. Theoretical radiation patterns of a subarray in the configuration of a cross are presented

Key polynomials for simple extensions of valued fields

Let $\iota:K\hookrightarrow L\cong K(x)$ be a simple transcendental extension of valued fields, where $K$ is equipped with a valuation $\nu$ of rank 1. That is, we assume given a rank 1 valuation $\nu$ of $K$ and its extension $\nu'$ to $L$. Let $(R_\nu,M_\nu,k_\nu)$ denote the valuation ring of $\nu$. The purpose of this paper is to present a refined version of MacLane's theory of key polynomials, similar to those considered by M. Vaqui\'e, and reminiscent of related objects studied by Abhyankar and Moh (approximate roots) and T.C. Kuo. Namely, we associate to $\iota$ a countable well ordered set $$\mathbf{Q}=\{Q_i\}_{i\in\Lambda}\subset K[x];$$ the $Q_i$ are called {\bf key polynomials}. Key polynomials $Q_i$ which have no immediate predecessor are called {\bf limit key polynomials}. Let $\beta_i=\nu'(Q_i)$. We give an explicit description of the limit key polynomials (which may be viewed as a generalization of the Artin--Schreier polynomials). We also give an upper bound on the order type of the set of key polynomials. Namely, we show that if $\operatorname{char}\ k_\nu=0$ then the set of key polynomials has order type at most $\omega$, while in the case $\operatorname{char}\ k_\nu=p>0$ this order type is bounded above by $\omega\times\omega$, where $\omega$ stands for the first infinite ordinal.Comment: arXiv admin note: substantial text overlap with arXiv:math/060519

Ballistic Localization in Quasi-1D Waveguides with Rough Surfaces

Structure of eigenstates in a periodic quasi-1D waveguide with a rough surface is studied both analytically and numerically. We have found a large number of "regular" eigenstates for any high energy. They result in a very slow convergence to the classical limit in which the eigenstates are expected to be completely ergodic. As a consequence, localization properties of eigenstates originated from unperturbed transverse channels with low indexes, are strongly localized (delocalized) in the momentum (coordinate) representation. These eigenstates were found to have a quite unexpeted form that manifests a kind of "repulsion" from the rough surface. Our results indicate that standard statistical approaches for ballistic localization in such waveguides seem to be unappropriate.Comment: 5 pages, 4 figure

Impurity Effects in Two-Electron Coupled Quantum Dots: Entanglement Modulation

We present a detailed analysis of the electronic and optical properties of two-electron quantum dots with a two-dimensional Gaussian confinement potential. We study the effects of Coulomb impurities and the possibility of manipulate the entanglement of the electrons by controlling the confinement potential parameters. The degree of entanglement becomes highly modulated by both the location and charge screening of the impurity atom, resulting two regimes: one of low entanglement and other of high entanglement, with both of them mainly determined by the magnitude of the charge. It is shown that the magnitude of the oscillator strength of the system could provide an indication of the presence and characteristics of impurities that could largely influence the degree of entanglement of the system.Comment: Regular Article (Journal of Physics B, in press), 9 pages, 10 figure