Scattering matrices and Weyl functions of quasi boundary triples

AbstractWe identify and investigate isoscattering strings of concatenating quantum graphs possessing n units and 2n infinite external leads. We give an insight into the principles of designing large graphs and networks for which the isoscattering properties are preserved for $$n \rightarrow \infty $$ n → ∞ . The theoretical predictions are confirmed experimentally using $$n=2$$ n = 2 units, four-leads microwave networks. In an experimental and mathematical approach our work goes beyond prior results by demonstrating that using a trace function one can address the unsettled until now problem of whether scattering properties of open complex graphs and networks with many external leads are uniquely connected to their shapes. The application of the trace function reduces the number of required entries to the $$2n \times 2n $$ 2 n × 2 n scattering matrices $${\hat{S}}$$ S ^ of the systems to 2n diagonal elements, while the old measures of isoscattering require all $$(2n)^2$$ ( 2 n ) 2 entries. The studied problem generalizes a famous question of Mark Kac “Can one hear the shape of a drum?”, originally posed in the case of isospectral dissipationless systems, to the case of infinite strings of open graphs and networks.

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Similarity between two scattering matrices

Electronics Letters ◽

10.1049/el:20010104 ◽

2001 ◽

Vol 37 (3) ◽

pp. 193 ◽

Cited By ~ 77

Author(s):

Jian Yang ◽

Ying-Ning Peng ◽

Shi-Ming Lin

Keyword(s):

Scattering Matrices

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Insertion Loss and Acoustic Reflection Expressed by Scattering Matrices with Energy-Dissipation for Surface Acoustic Unidirectional Interdigital-Transducers

Japanese Journal of Applied Physics ◽

10.1143/jjap.32.2329 ◽

1993 ◽

Vol 32 (Part 1, No. 5B) ◽

pp. 2329-2332

Author(s):

Takashi Shiba ◽

Yoshihiro Yamada ◽

Jun Yamada ◽

Kouji Oda

Keyword(s):

Energy Dissipation ◽

Insertion Loss ◽

Acoustic Reflection ◽

Scattering Matrices

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Method for computing waveguide scattering matrices in the vicinity of thresholds

St Petersburg Mathematical Journal ◽

10.1090/s1061-0022-2014-01332-5 ◽

2014 ◽

Vol 26 (1) ◽

pp. 91-116 ◽

Cited By ~ 6

Author(s):

B. A. Plamenevskiǐ ◽

A. S. Poretskiǐ ◽

O. V. Sarafanov

Keyword(s):

Scattering Matrices

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On normalization of scattering matrices of polarized radiation

Journal of Quantitative Spectroscopy and Radiative Transfer ◽

10.1016/j.jqsrt.2005.08.001 ◽

2006 ◽

Vol 101 (1) ◽

pp. 159-165 ◽

Cited By ~ 6

Author(s):

I.A. Vasilieva

Keyword(s):

Scattering Matrices ◽

Polarized Radiation

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MODELING THE FREQUENCY CHARACTERISTICS OF THE QUADRATURE THREE-LOOP L-BAND WAVELENGTH BRIDGE

Электросвязь ◽

10.34832/elsv.2021.22.9.008 ◽

2021 ◽

Author(s):

Л.В. АЛЕКСЕЙЧИК ◽

Н.В. АНДРИЕВСКИЙ

Keyword(s):

Transmission Lines ◽

Electric Circuit ◽

Wave Resistance ◽

Frequency Characteristics ◽

Excitation Mode ◽

S Matrix ◽

Scattering Matrices ◽

Standard Wave ◽

Strip Lines ◽

Algebraic Summation

Представлены результаты численного моделирования частотныххарактеристик квадратурного трехшлейфового моста (КШМ) L-диапазона, выполненного на основе симметричной полосковой линии с воздушным заполнением. Цель работы - установление допустимого уровня вносимых тепловых потерь полосковых линий (или других типов линий передачи), не оказывающих заметного влияния на рабочие характеристики КШМ, удовлетворяющие требуемым параметрам. Метод расчета основан на принципе декомпозиции электрической цепи КШМ на шесть симметричных 6-полюсников, три из которых соответствуют нечетной моде возбуждения КШМ, а три других - четной моде возбуждения КШМ. Алгебраическое суммирование матриц рассеяния указанных мод позволило получить частотные характеристики результирующей S-матрицы рассеяния КШМ. Нормирование S-матрицы к стандартному волновому сопротивлению 50 Ом выполнено с помощью вычисления собственных значений матриц рассеяния эквивалентных 4-полюсников КШМ. Моделирование проведено в среде LabVIEW. The paper presents the results of numerical simulation of the frequency characteristics of the L-range quadrature three-loop bridge (QLB), based on the symmetric striped line with air filling. The purpose of the study is to establish the permissible level of introduced thermal losses of strip lines (or other types of transmission lines) that do not significantly affect the performance characteristics of the QLB, satisfying the required parameters. The calculation method is based on the principle of decomposition of the QLB electric circuit into six symmetric 6-poles, three of which correspond to the odd excitation mode of the QLB, and the other three correspond to the even excitation mode of the QLB. Algebraic summation of the scattering matrices of these modes made it possible to obtain frequency characteristics of the resulting S-scattering matrix of the qLb. The normalization of the S-matrix to the standard wave resistance of 50 Ohms was carried out using the calculation of the eigenvalues of the scattering matrices of equivalent 4-poles of the QLB. The simulation was carried out in the LabVIEW environment.

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