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We derive the beam tracing and profile evolution for the propagation of any localised beam with arbitrary profile through an inhomogeneous cold plasma. We recover standard Gaussian beam-tracing, with an additional PDE describing the…
Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete…
Beam propagation beyond the paraxial approximation is studied in an optically written waveguide structure. The waveguide structure that leads to diffractionless light propagation, is imprinted on a medium consisting of a five-level atomic…
Scalar lattice gauge theories are models for scalar fields with local gauge symmetries. No fundamental gauge fields, or link variables in a lattice regularization, are introduced. The latter rather emerge as collective excitations composed…
We examine an extension to the theory of Gaussian wave packet dynamics in a one-dimensional potential by means of a sequence of time dependent displacement and squeezing transformations. Exact expressions for the quantum dynamics are found,…
We derive an exact expression for the partition function of the su(m) Haldane-Shastry spin chain, which we use to study the density of levels and the distribution of the spacing between consecutive levels. Our computations show that when…
The paper presents an ab initio account of the paraxial complex geometrical optics (CGO) in application to a scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic…
In Parts I and II we showed that e, $\nu$ propagators can be derived from rotation invariant projection operators, thereby providing examples of how quantities with spacetime symmetry can be obtained by constraining rotationally symmetric…
We present the shock-free wave propagation requirements for massless fields. First, we briefly argue how the "completely exceptional" approach, originally developed to study the characteristics of hyperbolic systems in 1+1 dimensions, can…
We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…
We increase the scope of previous work on change of basis between finite bases of polynomials by defining ascending and descending bases and introducing three techniques for defining them from known ones. The minimum degrees of polynomials…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in…
Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
We investigate light propagation through materials with periodically modulated gain/loss profile in both transverse and longitudinal directions, i.e. in material with two-dimensional modulation in space. We predict effects of…
In next-generation wireless networks, the combination of electrically large radiating apertures and high-frequency transmission extends the radiating near-field region around the transmitter. In this region, unlike in the far field, the…
Totally positive matrices are related with the shape preserving representations of a space of functions. The normalized B-basis of the space has optimal shape preserving properties. B-splines and rational Bernstein bases are examples of…
We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear…
Analogous coherent states are deduced from classical optical fields on curved surface in this paper. The Gaussian laser beam, as a fundamental mode, cannot be adequately simulated by coherent states due to their inherent diffraction in flat…