The defocusing mechanism of isochronous resonances

We present a numerical study concerning the defocusing mechanism of isochronous resonance island chains in the presence of two permanent robust tori. The process is initialized and concluded through bifurcations of fixed points located on the robust tori. Our approach is based on a Hamiltonian system derived from the resonant normal form. Choosing a convenient parameter in this system, we are able to depict a comprehensive analysis of the dynamics of the problem. (c) 2004 Elsevier B.V. All rights reserved.

Tunneling among rotation tori

We consider an integrable Hamiltonian system generated by the resonant normal form in order to study a particular mechanism of tunneling. We isolated near doublets of energy corresponding to rotation tori of the classical dynamics counterpart and the degeneracies breakdown is attributed to rotation-rotation tunneling. (C) 2008 Elsevier B.V. All rights reserved.

Tunneling among rotation tori

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Interference of robust tori on the resonance overlap

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Controle de dinâmica caótica com toros robustos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Elements of Non-Linear Hamiltonian Dynamics

In this paper we present a set of generic results on Hamiltonian non-linear dynamics. We show the necessary conditions for a Hamiltonian system to present a non-twist scenario and from that we introduce the isochronous resonances. The generality of these resonances is shown from the Hamiltonian given by the Birkhof-Gustavson normal form, which can be considered a toy model, and from an optic system governed by the non-linear map of the annular billiard. We also define a special kind of transport barrier called robust torus. The meanders and shearless curves are also presented and we show the most robust shearless barrier associated with the rotation numbers.

Optical waveguide and cavity effects on whispering-gallery mode resonances in a ZnO nanonail

Spatially resolved cathodoluminescence (CL) study of a ZnO nanonail, having thin shank, tapered neck, and hexagonal head sections, is reported. Monochromatic imaging and line scan profiling indicate that the wave guiding and leaking from growth imperfections in addition to the oxygen deficiency variation determine the spatial contrast of CL emissions. Occurrence of resonance peaks at identical wavelengths regardless of CL-excitation spots is inconsistent with the whispering-gallery mode (WGM) resonances of a two-dimensional cavity in the finite difference time domain simulation. However, three dimensioanl cavity simulation produced WGM peaks that are consistent with the experimental spectra, including transverse-electric resonances that are comparable to transverse-magnetic ones.

Predicting the localized surface plasmon resonances of spherical nanoparticles on substrate : electrostatic eigenmode method

We present experimental results that demonstrate that the wavelength of the fundamental localised surface plasmon resonance for spherical gold nanoparticles on glass can be predicted using a simple, one line analytical formula derived from the electrostatic eigenmode method. This allows the role of the substrate in lifting mode degeneracies to be determined, and the role of local environment refractive indices on the plasmon resonance to be investigated. The effect of adding silica to the casting solution in minimizing nanopaticle agglomeration is also discussed.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Search for WW and WZ Resonances Decaying to Electron, Missing ET, and Two Jets in pp̅ Collisions at √s=1.96 TeV.

Using data from 2.9  fb-1 of integrated luminosity collected with the CDF II detector at the Tevatron, we search for resonances decaying into a pair of on-shell gauge bosons, WW or WZ, where one W decays into an electron and a neutrino, and the other boson decays into two jets. We observed no statistically significant excess above the expected standard model background, and we set cross section limits at 95% confidence level on G* (Randall-Sundrum graviton), Z′, and W′ bosons. By comparing these limits to theoretical cross sections, mass exclusion regions for the three particles are derived. The mass exclusion regions for Z′ and W′ are further evaluated as a function of their gauge coupling strength.

Search for WW and WZ Resonances Decaying to Electron, Missing ET, and Two Jets in pp̅ Collisions at √s=1.96 TeV.

Using data from 2.9/fb of integrated luminosity collected with the CDF II detector at the Tevatron, we search for resonances decaying into a pair of on-shell gauge bosons, WW or WZ, where one W decays into an electron and a neutrino, and the other boson decays into two jets. We observed no statistically significant excess above the expected standard model background, and we set cross section limits at 95% confidence level on G*(Randall-Sundrum graviton), Z', and W' bosons. By comparing these limits to theoretical cross sections, mass exclusion regions for the three particles are derived. The mass exclusion regions for Z' and W' are further evaluated as a function of their gauge coupling strength.

Search for High-Mass Resonances Decaying to Dimuons at CDF

We present a search for high-mass neutral resonances using dimuon data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ collected in {$p\bar p$} collisions at {$\sqrt{s}$ = 1.96 TeV} by the CDF II detector at the Fermilab Tevatron. No significant excess above the standard model expectation is observed in the dimuon invariant-mass spectrum. We set 95% confidence level upper limits on $\sigma \cdot BR (p \bar{p} \to X \to \mu \bar{\mu})$, where $X$ is a boson with spin 0, 1, or 2. Using these cross section limits, we determine lower mass limits on sneutrinos in R-parity-violating supersymmetric models, $Z'$ bosons, and Kaluza-Klein gravitons in the Randall-Sundrum model.