Related papers: The WKB Approximation without Divergences
The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without assuming convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many interesting…
In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient…
The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB…
Regularization techniques for the numerical solution of inverse scattering problems in two space dimensions are discussed. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of…
The multichannel scattering problem in an adiabatic representation is considered. The non-adiabatic coupling matrix is assumed to have a non-trivial constant asymptotic behavior at large internuclear separations. The asymptotic solutions at…
Solutions in the form of series expansion, as the Born approximation, are very useful for describing time-independent scattering of quantum particles. In this work, it is mathematically demonstred that such solutions, when applied to…
Scattering theory has had a major roll in twentieth century mathematical physics. Mathematical modeling and algorithms of direct,- and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms…
This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
In this work, we investigate time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that is valid in the limit as…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
An adaptation of the WKB method in the deformation quantization formalism is presented with the aim to obtain an approximate technique of solving the eigenvalue problem for energy in the phase space quantum approach. A relationship between…
Scattering problems for periodic structures have been studied a lot in the past few years. A main idea for numerical solution methods is to reduce such problems to one periodicity cell. In contrast to periodic settings, scattering from…
Scattering off the edge of a composite particle or finite-range interaction can precede that off its center. An effective theory treatment with pointlike particles and contact interactions must find that the scattered experimental wave is…
Using a representation of multichannel quantum defect theory in terms of a quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show, that…
We show that the enhancement of backscattering responsible for the weak localization is accompanied by reduction of the scattering in other directions. A simple quasiclassical interpretation of this phenomenon is presented in terms of a…
Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…
We extract cluster structures and establish spectral coordinates from rank 3 WKB spectral networks $\mathcal W(\varphi,\vartheta)$ when zeros of $\varphi(z)$ are almost on a line in the complex plane. Then, we provide solutions to the…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
This paper focuses on the stability analysis of WKB approximate solutions in geometric optics with the absence of strong transparency conditions. We introduce a compatible condition and a singular localization method which allows us to…