In this paper, we extend a recently proposed scenario decomposition algorithm (Ahmed (2013)) for risk-neutral 0-1 stochastic programs to the risk-averse setting. Specifically, we consider risk-averse 0-1 stochastic programs with objective functions based on coherent risk measures. Using a dual representation of a coherent risk measure, we first derive an equivalent minimax reformulation of the ...

We propose an iterative method for in-situ optical testing under partially coherent illumination that relies on the rapid computation of aerial images. In this method a known pattern is imaged with the test optic at several planes through focus. A model is created that iterates through possible aberration maps until the through-focus series of aerial images matches the experimental result. The ...

We have constructed the coherent state of U(N, 1) , which is an extension of the Barut-Girardello (BG) coherent state of SU(1, 1), in our previous paper. However there is a restriction that the eigenvalue of the Casimir operator is natural number. In this paper we construct the coherent state in the analytic representation to overcome this restriction. Next we show that the measure of the BG co...

Affine variables, which have the virtue of preserving the positivedefinite character of matrix-like objects, have been suggested as replacements for the canonical variables of standard quantization schemes, especially in the context of quantum gravity. We develop the kinematics of such variables, discussing suitable coherent states, their associated resolution of unity, polarizations, and final...

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture is developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic...

We construct the action-angle variables of a classical integrable model dened on complex projective phase space and calculate the quantum mechanical propagator in the coherent state path integral representation using the stationary phase approximation. We show that the resulting expression for the propagator coincides with the exact propagator which was obtained by solving the time-dependent Sc...

We present a computation of the coherent state path integral for a generic linear system using “functional methods” (as opposed to discrete time approaches). The Gaussian phase space path integral is formally given by a determinant built from a first-order differential operator with coherent state boundary conditions. We show how this determinant can be expressed in terms of the symplectic tran...

The spin coherent state path integral describing the dynamics of a spin-12system in a magnetic field of arbitrary time-dependence is considered. Defining the path integral as the limit of a Wiener regularized expression, the semiclassical approximation leads to a continuous minimal action path with jumps at the endpoints. The resulting semiclassical propagator is shown to coincide with the exac...

The semiclassical propagator cannot be directly obtained in Fock state representation, since the Fock states form a discrete basis rather than a continuous one as required by the path integral formalism. To solve this problem, we first derive a semiclassical propagator in quadrature representation and then project the result on Fock states. The quadrature eigenstates |q 〉 ≡ |q1, . . . , qL 〉 an...

A generalized formulation of spontaneous emission and super-radiance effects in a free-electron laser is presented. We consider a stream of electrons of arbitrary temporal duration propagating through the undulator. The sum of the undulator synchrotron radiation emitted by individual wiggling electrons entering the wiggler at random, results in shot-noise in the radiation field. Using the waveg...