scholarly journals Higher-order Hamilton–Jacobi perturbation theory for anisotropic heterogeneous media: dynamic ray tracing in Cartesian coordinates

2018 ◽  
Vol 216 (3) ◽  
pp. 2044-2070 ◽  
Author(s):  
Einar Iversen ◽  
Bjørn Ursin ◽  
Teemu Saksala ◽  
Joonas Ilmavirta ◽  
Maarten V de Hoop
Keyword(s):  
Perturbation Theory ◽  
Ray Tracing ◽  
Heterogeneous Media ◽  
Higher Order ◽  
Cartesian Coordinates ◽  
Dynamic Ray Tracing

Higher-order dynamic ray tracing in ray-centred coordinates

2019 ◽  
Author(s):  
Einar Iversen ◽  
Bjørn Ursin ◽  
Teemu Saksala ◽  
Joonas Ilmavirta ◽  
Maarten V. de Hoop
Keyword(s):  
Ray Tracing ◽  
Higher Order ◽  
Dynamic Ray Tracing

scholarly journals Stochastic computation of g − 2 in QED

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ryuichiro Kitano ◽  
Hiromasa Takaura ◽  
Shoji Hashimoto
Keyword(s):  
Perturbation Theory ◽  
Numerical Computation ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Stochastic Perturbation ◽  
Higher Order ◽  
Feynman Diagrams ◽  
Perturbative Series ◽  
Physical Quantities

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

Expansions of the mildly relativistic dispersion function for nearly perpendicular electron cyclotron ray tracing

1999 ◽  
Vol 61 (1) ◽  
pp. 121-128 ◽  
Author(s):  
I. P. SHKAROFSKY
Keyword(s):  
Ray Tracing ◽  
Computer Programs ◽  
Higher Order ◽  
Electron Cyclotron ◽  
Dispersion Function ◽  
Relativistic Dispersion ◽  
Plasma Dispersion ◽  
Derivatives Of ◽  
Cyclotron Harmonic ◽  
Experienced Difficulty

To trace rays very close to the nth electron cyclotron harmonic, we need the mildly relativistic plasma dispersion function and its higher-order derivatives. Expressions for these functions have been obtained as an expansion for nearly perpendicular propagation in a region where computer programs have previously experienced difficulty in accuracy, namely when the magnitude of (c/vt)2 (ω−nωc)/ω is between 1 and 10. In this region, the large-argument expansions are not yet valid, but partial cancellations of terms occur. The expansion is expressed as a sum over derivatives of the ordinary dispersion function Z. New expressions are derived to relate higher-order derivatives of Z to Z itself in this region of concern in terms of a finite series.

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