1,087 research outputs found
Shilnikov Lemma for a nondegenerate critical manifold of a Hamiltonian system
We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic
critical manifold of a Hamiltonian system. Using this
result, trajectories with small energy shadowing chains of homoclinic
orbits to are represented as extremals of a discrete variational problem,
and their existence is proved. This paper is motivated by applications to the
Poincar\'e second species solutions of the 3 body problem with 2 masses small
of order . As , double collisions of small bodies correspond to
a symplectic critical manifold of the regularized Hamiltonian system
Metal-nanoparticle single-electron transistors fabricated using electromigration
We have fabricated single-electron transistors from individual metal
nanoparticles using a geometry that provides improved coupling between the
particle and the gate electrode. This is accomplished by incorporating a
nanoparticle into a gap created between two electrodes using electromigration,
all on top of an oxidized aluminum gate. We achieve sufficient gate coupling to
access more than ten charge states of individual gold nanoparticles (5-15 nm in
diameter). The devices are sufficiently stable to permit spectroscopic studies
of the electron-in-a-box level spectra within the nanoparticle as its charge
state is varied.Comment: 3 pages, 3 figures, submitted to AP
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