This paper investigates the generation of quadrature-squeezed states of light using a degenerate optical parametric amplifier ~DOPA! that is pumped by a focused Gaussian beam. The formulation that is presented facilitates the calculation of squeezing for an arbitrary local oscillator beam. This formulation also establishes a formal equivalence between the classical parametric gain and the measu...

Engineering mechanics formulations of aerospace industry problems overwhelmingly rely upon spatial averaging techniques. Crucial applications in the area of dynamic response analysis and stochastic estimation of material degradation can be cited as important cases. Integration procedures on finite domains underlie physically acceptable averaging processes. Unlike one-dimensional cases, integral...

In preparation for computational work with molecular orbitals written as linear combinaions of atomic orbitals, for first and second row atoms, we have developed a general procedure to parametrize linear combinations of Gaussian orbitals. We used a Gaussian transform, and a Gauss-Legendre quadrature, to express hydrogenic orbitals (with the correct long-range dependence for collisions) as contr...

The impact of homodyne and heterodyne crosstalk on transmission performance of optical space switches based on a Benes network is studied. The system power penalty is evaluated as a function of the switch size using a rigorous approach based on the Gaussian quadrature rules method. These results are used as a reference to assess the accuracy of other relevant methods, such as saddlepoint approx...

We define the statistical quadrature evolution (QE) method for multicarrier continuousvariable quantum key distribution (CVQKD). A multicarrier CVQKD protocol uses Gaussian subcarrier quantum continuous variables (CVs) for information transmission. The QE scheme utilizes the theory of mathematical statistics and statistical information processing. The QE model is based on the Gaussian quadratur...

We discuss some recent developments in the implementation of the Schwinger multichannel method for electron-molecule collision calculations. The evaluation of matrix elements involving the operator VGp+'V, previously accomplished by insertion of a Gaussian basis on either side of Gz+', is now done by direct numerical quadrature. This approach avoids the necessity of very large Gaussian basis se...

Gauss quadrature is a well-known method for estimating the integral of a continuous function with respect to a given measure as a weighted sum of the function evaluated at a set of node points. Gauss quadrature is traditionally developed using orthogonal polynomials. We show that Gauss quadrature can also be obtained as the solution to an infinite-dimensional linear program (LP): minimize the n...

Gauss and Clenshaw–Curtis quadrature, like Legendre and Chebyshev spectral methods, make use of grids strongly clustered at boundaries. From the viewpoint of polynomial approximation this seems necessary and indeed in certain respects optimal. Nevertheless such methods may “waste” a factor of π/2 with respect to each space dimension. We propose new nonpolynomial quadrature methods that avoid th...