najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1279Research ArticleMATHEMATICSМАТЕМАТИКАMethod of symmetric polynomials in the computations of scattering matrixBelyayevYu. N.

Oktyabrskii pr. 55, Syktyvkar-167001

ybelyayev@mail.ruSyktyvkar State UniversityRussian Federation20132108202543306312Copyright © Belyayev Y.N., 20252025Belyayev Y.N.Belyayev Y.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1279

The method for calculating any analytic matrix function by means of symmetric polynomials is presented. The method of symmetric polynomials (MSP) is applied to the calculation of the fundamental matrix of a differential equations system. The scaling method is developed for computation of the scattering matrix. An analytical estimate of the scaling parameter, allowing the calculation of the matrix exponential with the required reliability and accuracy is obtained. This parameter depends on the matrix order n, the value of the matrix elements and layer thickness.

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The authors declare that there are no conflicts of interest present.