Fabrication of large addition energy quantum dots in graphene

We present a simple technique to fabricate graphene quantum dots in a cryostat. It relies upon the controlled rupture of a suspended graphene sheet subjected to the application of a large electron current. This results in the in-situ formation of a clean and ultra-narrow constriction, which hosts one quantum dot, and occasionally a few quantum dots in series. Conductance spectroscopy indicates that individual quantum dots can possess an addition energy as large as 180 meV and a level spacing as large as 25 meV. Our technique has several assets: (i) the dot is suspended, thus the electrostatic influence of the substrate is reduced, and (ii) contamination is minimized, since the edges of the dot have only been exposed to the vacuum in the cryostat.Comment: Improved version. To appear in Applied Physics Letter

A few things I learnt from Jurgen Moser

A few remarks on integrable dynamical systems inspired by discussions with Jurgen Moser and by his work.Comment: An article for the special issue of "Regular and Chaotic Dynamics" dedicated to 80-th anniversary of Jurgen Mose

Symmetry breaking in a mechanical resonator made from a carbon nanotube

Nanotubes behave as semi-flexible polymers in that they can bend by a sizeable amount. When integrating a nanotube in a mechanical resonator, the bending is expected to break the symmetry of the restoring potential. Here we report on a new detection method that allows us to demonstrate such symmetry breaking. The method probes the motion of the nanotube resonator at nearly zero-frequency; this motion is the low-frequency counterpart of the second overtone of resonantly excited vibrations. We find that symmetry breaking leads to the spectral broadening of mechanical resonances, and to an apparent quality factor that drops below 100 at room temperature. The low quality factor at room temperature is a striking feature of nanotube resonators whose origin has remained elusive for many years. Our results shed light on the role played by symmetry breaking in the mechanics of nanotube resonators.Comment: manuscript and supplementary material, 7 figure

High-frequency nanotube mechanical resonators

We report on a simple method to fabricate high-frequency nanotube mechanical resonators reproducibly. We measure resonance frequencies as high as 4.2 GHz for the fundamental eigenmode and 11 GHz for higher order eigenmodes. The high-frequency resonances are achieved using short suspended nanotubes and by introducing tensile stress in the nanotube. These devices allow us to determine the coefficient of the thermal expansion of an individual nanotube, which is negative and is about -0.7E-5 1/K at room temperature. High-frequency resonators made of nanotubes hold promise for mass sensing and experiments in the quantum limit

Calculation of three-dimensional compressible laminar and turbulent boundary layers. Calculation of three-dimensional compressible boundary layers on arbitrary wings

A very general method for calculating compressible three-dimensional laminar and turbulent boundary layers on arbitrary wings is described. The method utilizes a nonorthogonal coordinate system for the boundary-layer calculations and includes a geometry package that represents the wing analytically. In the calculations all the geometric parameters of the coordinate system are accounted for. The Reynolds shear-stress terms are modeled by an eddy-viscosity formulation developed by Cebeci. The governing equations are solved by a very efficient two-point finite-difference method used earlier by Keller and Cebeci for two-dimensional flows and later by Cebeci for three-dimensional flows

Compressibility and probabilistic proofs

We consider several examples of probabilistic existence proofs using compressibility arguments, including some results that involve Lov\'asz local lemma.Comment: Invited talk for CiE 2017 (full version

Non-Zhang-Rice singlet character of the first ionization state of T-CuO

We argue that tetragonal CuO (T-CuO) has the potential to finally settle long-standing modelling issues for cuprate physics. We compare the one-hole quasiparticle (qp) dispersion of T-CuO to that of cuprates, in the framework of the strongly-correlated ($U_{dd}\rightarrow \infty$) limit of the three-band Emery model. Unlike in CuO$_2$, magnetic frustration in T-CuO breaks the $C_4$ rotational symmetry and leads to strong deviations from the Zhang-Rice singlet picture in parts of the reciprocal space. Our results are consistent with angle-resolved photoemission spectroscopy data but in sharp contradiction to those of a one-band model previously suggested for them. These differences identify T-CuO as an ideal material to test a variety of scenarios proposed for explaining cuprate phenomenology.Comment: 4 pages, 2 figure

Persistence of Diophantine flows for quadratic nearly-integrable Hamiltonians under slowly decaying aperiodic time dependence

The aim of this paper is to prove a Kolmogorov-type result for a nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists of the possibility to choose an arbitrarily small decaying coefficient, consistently with the perturbation size.Comment: Several corrections in the proof with respect to the previous version. Main statement unchange