Nanomechanical resonators operating as charge detectors in the nonlinear regime

We present measurements on nanomechanical resonators machined from Silicon-on-Insulator substrates. The resonators are designed as freely suspended Au/Si beams of lengths on the order of 1 - 4 um and a thickness of 200 nm. The beams are driven into nonlinear response by an applied modulation at radio frequencies and a magnetic field in plane. The strong hysteresis of the magnetomotive response allows sensitive charge detection by varying the electrostatic potential of a gate electrode.Comment: 8 pages, 6 figure

On the uniqueness of sign changing bound state solutions of a semilinear equation

We establish the uniqueness of the higher radial bound state solutions of \Delta u +f(u)=0,\quad x\in \RR^n. \leqno(P) We assume that the nonlinearity $f\in C(-\infty,\infty)$ is an odd function satisfying some convexity and growth conditions, and either has one zero at $b>0$, is non positive and not identically 0 in $(0,b)$, and is differentiable and positive $[b,\infty)$, or is positive and differentiable in $[0,\infty)$

Sturm-Liouville operators on time scales

We establish the connection between Sturm-Liouville equations on time scales and Sturm--Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm-Liouville equations on time scales which have been obtained by various authors in the past.Comment: 12 page

Form factors and photoproduction amplitudes

We examine the use of phenomenological form factors in tree level amplitudes for meson photoproduction. Two common recipes are shown to be fundamentally incorrect. An alternate form consistent with gauge invariance and crossing symmetry is proposed.Comment: To be published in PR

Photo- and Electron-Production of Mesons on Nucleons and Nuclei

In these lectures I will show some results obtained with the chiral unitary approach applied to the photo and electroproduction of mesons. The results for photoproduction of $\eta \pi^0 p$ and $K^0 \pi^0 \Sigma^+$, together with related reactions will be shown, having with common denominator the excitation of the $\Delta(1700)$ resonance which is one of those dynamically generated in the chiral unitary approach. Then I will show results obtained for the $e^+ e^- \to \phi f_0(980)$ reaction which reproduce the bulk of the data except for a pronounced peak, giving support to a new mesonic resonance, X(2175). Results will also be shown for the electromagnetic form factors of the $N^*(1535)$ resonance, also dynamically generated in this approach. Finally, I will show some results on the photoproduction of the $\omega$ in nuclei, showing that present experimental results claiming a shift of the $\omega$ mass in the medium are tied to a particular choice of background and are not conclusive. One the other hand, the same experimental results show unambiguously a huge increase of the $\omega$ width in the nuclear medium.Comment: Lecture at the "International School of Nuclear Physics", 29th Course Quarks in Hadrons and Nuclei, Erice, Italy, September 2007. Note added in Proofs concerning the mixed events technique and other comments on omega productio

Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper box

We analyse the quantum dynamics of a micromechanical resonator capacitively coupled to a Cooper box. With appropriate quantum state control of the Cooper box, the resonator can be driven into a superposition of spatially separated states. The Cooper box can also be used to probe the environmentally-induced decoherence of the resonator superposition state.Comment: 4 pages, 3 figure

Carbon Nanotubes as Nanoelectromechanical Systems

We theoretically study the interplay between electrical and mechanical properties of suspended, doubly clamped carbon nanotubes in which charging effects dominate. In this geometry, the capacitance between the nanotube and the gate(s) depends on the distance between them. This dependence modifies the usual Coulomb models and we show that it needs to be incorporated to capture the physics of the problem correctly. We find that the tube position changes in discrete steps every time an electron tunnels onto it. Edges of Coulomb diamonds acquire a (small) curvature. We also show that bistability in the tube position occurs and that tunneling of an electron onto the tube drastically modifies the quantized eigenmodes of the tube. Experimental verification of these predictions is possible in suspended tubes of sub-micron length.Comment: 8 pages, 5 eps figures included. Major changes; new material adde

Nuclear shadowing at low photon energies

We calculate the shadowing effect in nuclear photoabsorption at low photon energies (1-3 GeV) within a multiple scattering approach. We avoid some of the high energy approximations that are usually made in simple Glauber theory like the narrow width and the eikonal approximation. We find that the main contribution to nuclear shadowing at low energies stems from $\rho^0$ mesons with masses well below their pole mass. We also show that the possibility of scattering in non forward directions allows for a new contribution to shadowing at low energies: the production of neutral pions as intermediate hadronic states enhances the shadowing effect in the onset region. For light nuclei and small photon energies they give rise to about 30% of the total shadowing effect.Comment: RevTeX, 16 pages including 6 eps figures; new calculation of effective pion propagator, negligible effect on results; version to be published in Phys. Rev.

Systematic Regge theory analysis of omega photoproduction

Systematic analysis of available data for $\omega$-meson photoproduction is given in frame of Regge theory. At photon energies above 20 GeV the $\gamma{+}p{\to}\omega{+}p$ reaction is entirely dominated by Pomeron exchange. However, it was found that Pomeron exchange model can not reproduce the $\gamma{+}p{\to}\rho{+}p$ and $\gamma{+}p{\to}\omega{+}p$ data at high energies simultaneously with the same set of parameters. The comparison between $\rho$ and $\omega$ data indicates a large room for meson exchange contribution to $\omega$-meson photoproduction at low energies. It was found that at low energies the dominant contribution comes from $\pi$ and $f_2$-meson exchanges. There is smooth transition between the meson exchange model at low energies and Regge theory at high energies.Comment: 7 pages, 8 figures, revtex