A note on the calculation of the effective range

The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining the effective range, by fitting a numerical solution of the Schr\"odinger equation to known asymptotic boundary conditions, can be modified to include the first order contribution of a long range interaction.Comment: 4 page

Self-aligned fabrication process for silicon quantum computer devices

We describe a fabrication process for devices with few quantum bits (qubits), which are suitable for proof-of-principle demonstrations of silicon-based quantum computation. The devices follow the Kane proposal to use the nuclear spins of 31P donors in 28Si as qubits, controlled by metal surface gates and measured using single electron transistors (SETs). The accurate registration of 31P donors to control gates and read-out SETs is achieved through the use of a self-aligned process which incorporates electron beam patterning, ion implantation and triple-angle shadow-mask metal evaporation

Formation of atomic tritium clusters and condensates

We present an extensive study of the static and dynamic properties of systems of spin-polarized tritium atoms. In particular, we calculate the two-body |F,m_F>=|0,0> s-wave scattering length and show that it can be manipulated via a Feshbach resonance at a field strength of about 870G. Such a resonance might be exploited to make and control a Bose-Einstein condensate of tritium in the |0,0> state. It is further shown that the quartet tritium trimer is the only bound hydrogen isotope and that its single vibrational bound state is a Borromean state. The ground state properties of larger spin-polarized tritium clusters are also presented and compared with those of helium clusters.Comment: 5 pages, 3 figure

Systems, methods, and apparatus of a low conductance silicon micro-leak for mass spectrometer inlet

Systems, methods and apparatus are provided through which in some embodiments a mass spectrometer micro-leak includes a number of channels fabricated by semiconductor processing tools and that includes a number of inlet holes that provide access to the channels

Systems, Methods, and Apparatus of a Low Conductance Silicon Micro-Leak for Mass Spectrometer Inlet

Systems, methods and apparatus are provided through which in some embodiments a mass spectrometer micro-leak includes a number of channels fabricated by semiconductor processing tools and that includes a number of inlet holes that provide access to the channels

The variable phase method used to calculate and correct scattering lengths

It is shown that the scattering length can be obtained by solving a Riccati equation derived from variable phase theory. Two methods of solving it are presented. The equation is used to predict how long-range interactions influence the scattering length, and upper and lower bounds on the scattering length are determined. The predictions are compared with others and it is shown how they may be obtained from secular perturbation theory.Comment: 7 pages including 3 figure

Hydrodynamic object recognition using pressure sensing

Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing

Stability of Waves in Multi-component DNLS system

In this work, we systematically generalize the Evans function methodology to address vector systems of discrete equations. We physically motivate and mathematically use as our case example a vector form of the discrete nonlinear Schrodinger equation with both nonlinear and linear couplings between the components. The Evans function allows us to qualitatively predict the stability of the nonlinear waves under the relevant perturbations and to quantitatively examine the dependence of the corresponding point spectrum eigenvalues on the system parameters. These analytical predictions are subsequently corroborated by numerical computations.Comment: to appear Journal of Physics A: Mathematical and Theoretica