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Related papers: The WKB Approximation without Divergences

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We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…

Machine Learning · Computer Science 2025-05-20 Borong Zhang , Martín Guerra , Qin Li , Leonardo Zepeda-Núñez

This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…

Numerical Analysis · Mathematics 2024-08-07 Borong Zhang , Leonardo Zepeda-Núñez , Qin Li

The master equation for a damped spin well known from the theory of superradiance, is written as a finite-difference equation and solved by a WKB-like method. The propagator thus obtained looks like the van Vleck propagator of a certain…

chao-dyn · Physics 2009-10-31 Petr A. Braun , Daniel Braun , Fritz Haake

Inspired by the problem of Planckian scattering we describe a classical effective field theory for weak ultra relativistic scattering in which field propagation is instantaneous and transverse and the particles' equations of motion localize…

High Energy Physics - Theory · Physics 2011-08-08 Barak Kol

The Wentzel-Kramers-Brillouin (WKB) approximation is frequently used to explore the mechanics of the cochlea. As opposed to numerical strategies, the WKB approximation facilitates analysis of model results through interpretable closed-form…

Biological Physics · Physics 2024-01-03 Brian L. Frost

This paper presents the derivation of Schwinger's gauge invariant result of $Im \cal{L}_{eff}$ upto one loop approximation, for particle production in an uniform electric field through the method of complex trajectory WKB approximation…

General Relativity and Quantum Cosmology · Physics 2016-12-21 S. Biswas , A. Shaw , B. Modak

The WKB approximation for deformed space with minimal length is considered. The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in presence of deformation is that the WKB approximation is valid for intermediate…

Quantum Physics · Physics 2009-11-11 T. V. Fityo , I. O. Vakarchuk , V. M. Tkachuk

We present a significant improvement to a time-dependent WKB (TDWKB) formulation developed by Boiron and Lombardi [JCP {\bf108}, 3431 (1998)] in which the TDWKB equations are solved along classical trajectories that propagate in the complex…

Quantum Physics · Physics 2009-11-13 Yair Goldfarb , Jeremy Schiff , David J Tannor

Wentzel, Kramers, Brillouin (WKB) approximation for fractional systems is investigated in this paper using the fractional calculus. In the fractional case the wave function is constructed such that the phase factor is the same as the…

Mathematical Physics · Physics 2007-05-23 Eqab M. Rabei , Ibrahim M. A. Altarazi , Sami I. Muslih , Dumitru Baleanu

It is well-known that the standard WKB approximation fails to provide semiclassical solutions in the vicinity of turning points. However, turning points arise in many cosmological scenarios. In a previous work, we obtained a new class of…

General Relativity and Quantum Cosmology · Physics 2016-02-12 Antonin Coutant

The results of the development of an approximate approach, which can be considered as an analogue of the WKB method, are presented. This approach gives possibility to divide the electromagnetic field in structured waveguides into forward…

Accelerator Physics · Physics 2022-12-08 M. I. Ayzatsky

This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying…

Numerical Analysis · Mathematics 2025-06-30 Thuy T. Le , Phuong M. Nguyen , Loc H. Nguyen

We develop a spectral formulation and a stationary WKB approximation for calculating the probabilities of rare events (large deviations from the mean) in systems of reacting particles with infinite-range interaction, describable by a master…

Statistical Mechanics · Physics 2009-11-11 Michael Assaf , Baruch Meerson

This paper is concerned with the efficient numerical treatment of 1D stationary Schr\"odinger equations in the semi-classical limit when including a turning point of first order. For the considered scattering problems we show that the wave…

Numerical Analysis · Mathematics 2019-11-19 Anton Arnold , Kirian Döpfner

The Wentzel-Kramers-Brillouin (WKB) perturbative series, a widely used technique for solving linear waves, is typically divergent and at best, asymptotic, thus impeding predictions beyond the first few leading-order effects. Here, we report…

Quantum Physics · Physics 2022-02-23 B. Tripathi

We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…

Numerical Analysis · Mathematics 2023-07-06 Qinjing Qiu , Reiichiro Kawai

A \emph{double extrema form} of the calculus of variations is put forward in which only the smallest one of the finite differences is physically meaningful to represent the variational derivatives defined on the discrete points. The most…

Statistical Mechanics · Physics 2021-04-13 Q. H. Liu

The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…

Numerical Analysis · Mathematics 2020-08-05 Ken'ichiro Tanaka , Alexis Akira Toda

Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using…

Atomic Physics · Physics 2015-05-27 M. V. Volkov , N. Elander , E. Yarevsky , S. L. Yakovlev

We study the Klein paradox for the semi-classical Dirac operator on $\R$ with potentials having constant limits, not necessarily the same at infinity. Using the complex WKB method, the time-independent scattering theory in terms of incoming…

Spectral Theory · Mathematics 2007-11-21 Abdallah Khochman