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Linear response laws and causality (the effect cannot precede the cause) are of fundamental importance in physics. In the context of classical electrodynamics, students often have a difficult time grasping these concepts because the physics is obscured by the intermingling of the time and frequency domains. In this paper, we analyse the linear response laws and causality in the time and frequency domains with the aim of pedagogical clarity. We will show that it is easy to violate causality in the frequency domain by making a vanishing absorption approximation. Furthermore, we will show that there can be subtle differences between Fourier transformingMaxwell equations and using a monochromatic source function. We discuss how these concepts can be obscured and offer some suggestions to improve the situation. [ABSTRACT FROM AUTHOR]

The generator coordinatemethod in the Gaussian overlap approximation (GOA) is applied to a description of the nuclear quadrupole collective states. The full five-dimensional quadrupole tensor is used as a set of the generator coordinates. The integral Hill-Wheeler equation is reduced to a differential equation by using the Fourier transforms of the overlap and energy kernels. The differential Bohr Hamiltonian obtained this way is compared with that derived by the usual approach to the collective Hamiltonian in the GOA which does contain an additional approximation. The method of calculating the quantities which determine the Bohr Hamiltonian from the set of deformation-dependent intrinsic states is demonstrated. In particular, it appears that the moments of inertia at the quadrupole rotations are of the Yoccoz type. [ABSTRACT FROM AUTHOR]

We provide (partial) reconstruction formulas and discrete Fourier transforms for wavefunctions in standard Fock-Bargmann (holomorphic) phase-number representation from a finite number N of phase samples {&thetas;k = 2πk/N}N-1 k=0 for a given mean number p of particles. The resulting coherent state subsystem S = {|zk = p1/2 ei&thetas;k 〉} is complete (a frame) for truncated Hilbert spaces (finite number of particles) and reconstruction formulas are exact. For an unbounded number of particles, S is 'almost complete' (a pseudo-frame) and partial reconstruction formulas are provided along with a study of the accuracy of the approximation, which tends to be exact when p < N and/or N →∞. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating lower atmospheric refractivity under the nonstandard propagation conditions frequently encountered in low altitude maritime radar applications. The vertical structure of the refractive environment is modeled by using a five-parameter model, and the horizontal structure is modeled as range-independent. The electromagnetic propagation in the troposphere is simulated by using a split-step fast Fourier transform based on parabolic approximation to the wave equation. A global search marked as a modified genetic algorithm (MGA) for the 5 environmental parameters is performed by using a genetic algorithm (GA) integrated with a simulated annealing technique. The retrieved results from simulated runs demonstrate the ability of this method to make atmospheric refractivity estimations. A comparison with the classical GA and the Bayesian Markov Chain Monte Carlo (Bayesian-MCMC) technique shows that the MGA can not only shorten the inverse time but also improve the inverse precision. For real data cases, the inversion values do not match the reference data very well. The inverted profile, however, can be used to synoptically describe the real refractive structure. [ABSTRACT FROM AUTHOR]

The photoionization cross section of endohedral Xe@C60 over a Xe 4d giant resonance energy region, calculated in the time-dependent local density approximation, is compared with recent measurements (Kilcoyne et al 2010 Phys. Rev. Lett. 105 213001). An analysis based on the Fourier transforms of oscillatory cross sections is performed to derive a number of inherent similarities between the prediction and the data, including a large beating-type oscillation and several others of intermediate size. Results stress the need for more accurate measurements to access the wealth of information about the geometry of the system. [ABSTRACT FROM AUTHOR]

We investigate the accuracy of different common methods for calculating the momentum distribution of the nuclei following dissociation of H by a short, intense laser pulse. This analysis can be performed either exactly by projecting onto scattering states of the system or by using a Fourier transformation of the final wavefunction. When and how this Fourier transform is made determines the validity of the approximation. While the values of the total observables were comparable, the Fourier transform methods require further free propagation time to converge to the exact result. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of polarization properties, scattering properties and propagation properties of global positioning system (GPS) scattering signal over the rough sea surface. To investigate the polarization and the scattering properties, the scattering field and the bistatic scattering coefficient of modified Kirchhoff approximation using the tapered incident wave is derived in detail. In modeling the propagation properties of the GPS scattering signal in the evaporation duct, the initial field of parabolic equation traditionally computed by the antenna pattern using fast Fourier transform (FFT) is replaced by the GPS scattering field. And the propagation properties of the GPS scattering signal in the evaporation duct with different evaporation duct heights and elevation angles of GPS are discussed by the improved discrete mixed Fourier transform taking into account the sea surface roughness. [ABSTRACT FROM AUTHOR]

A novel three-dimensional wide-angle beam propagation method based on the split-step fast Fourier transform is developed. The formulation is based on the three-dimensional Helmholtz wave equation. Each propagation step is performed by utilizing both the FFT and split-step scheme. The solution of Helmholtz wave equation does not make the slowly varying envelope and one-way propagation approximations. To validate the efficiency and accuracy, numerical results for a propagation beam in a tilted step-index optical waveguide are compared with other beam propagation algorithms. [ABSTRACT FROM AUTHOR]