Related papers: The WKB Approximation without Divergences
We derive quantitative bounds in the Wasserstein distance for the approximation of stochastic integrals with respect to Hawkes processes by a normally distributed random variable. In the case of deterministic and non-negative integrands,…
Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…
We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover…
This paper is devoted to the analysis of propagation properties for the solutions of a one-dimensional non-local Schr\"odinger equation involving the fractional Laplace operator $(-d_x^2)^s$, $s\in(0,1)$. We adopt a classical WKB approach…
Periodic surface structures are nowadays standard building blocks of optical devices. If such structures are illuminated by aperiodic time-harmonic incident waves as, e.g., Gaussian beams, the resulting surface scattering problem must be…
This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…
In this paper, we propose a derivative-free Levenberg-Marquardt algorithm for nonlinear least squares problems, where the Jacobian matrices are approximated via orthogonal spherical smoothing. It is shown that the gradient models which use…
We formulate a ''minimal'' interpretational scheme for fairly general (minisuperspace) quantum cosmological models. Admitting as few exact mathematical structure as is reasonably possible at the fundamental level, we apply approximate…
Nonlinear WKB is a multiscale technique for studying locally-plane-wave solutions of nonlinear partial differential equations (PDE). Its application comprises two steps: (1) replacement of the original PDE with an extended system separating…
An approximate method is proposed for the recovery of a compactly supported spherically-symmetric potential from the set of fixed-energy phase-shifts known for all angular momenta. The method reduces the inverse scattering problem to a…
We explore the possibility of modifying the Lewis-Riesenfeld method of invariants developed originally to find exact solutions for time-dependent quantum mechanical systems for the situation in which an exact invariant can be constructed,…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
In this paper we propose recurrence relations for the dipole densities in QCD, which allows us to find these densities from the solution to the BFKL equation. We resolve these relations in the diffusion approximation for the BFKL kernel.…
A singular perturbation problem called WKB equation (Eq) $h^2u(x,h)-Q(x)u(x,h)=0$ is studied. $h>0$ is a small parameter. Investigation of (Eq) has long history. Recently it has developed by a new method named "Exact WKB Analysis" based on…
This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced…
It is shown that tailored breaking of the translational symmetry through weak scattering in waveguides and optical fibers can control chromatic dispersions of the individual modes at any order; thereby, it overcomes the problem of coherent…
We demonstrate the successful use of scattering representations without further compression for simulation-based inference (SBI) with images (i.e. field-level), illustrated with a cosmological case study. Scattering representations provide…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
Nonperturbative polaron variational methods are applied, within the so-called particle or worldline representation of relativistic field theory, to study scattering in the context of the scalar Wick - Cutkosky model. Important features of…