scholarly journals Direct computation of scattering matrices for general quantum graphs

2010 ◽  
Vol 828 (3) ◽  
pp. 515-535 ◽  
Author(s):  
V. Caudrelier ◽  
E. Ragoucy
Keyword(s):  
Quantum Graphs ◽  
Direct Computation ◽  
General Quantum ◽  
Scattering Matrices

scholarly journals Isoscattering strings of concatenating graphs and networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michał Ławniczak ◽  
Adam Sawicki ◽  
Małgorzata Białous ◽  
Leszek Sirko
Keyword(s):  
Trace Function ◽  
Quantum Graphs ◽  
Mathematical Approach ◽  
Large Graphs ◽  
Graphs And Networks ◽  
Scattering Matrices ◽  
Theoretical Predictions ◽  
Infinite Strings ◽  
Microwave Networks ◽  
Insight Into

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.

Green function approach for general quantum graphs

2003 ◽  
Vol 36 (42) ◽  
pp. L545-L551 ◽  
Author(s):  
Alexandre G M Schmidt ◽  
Bin Kang Cheng ◽  
M G E da Luz
Keyword(s):  
Green Function ◽  
Function Approach ◽  
Quantum Graphs ◽  
General Quantum ◽  
Green Function Approach

scholarly journals Geometric properties of quantum graphs and vertex scattering matrices

2010 ◽  
Vol 30 (3) ◽  
pp. 295 ◽  
Author(s):  
Pavel Kurasov ◽  
Marlena Nowaczyk
Keyword(s):  
Quantum Graphs ◽  
Geometric Properties ◽  
Scattering Matrices

Wave-Mode Coordinates and Scattering Matrices for Wave Propagation.

1986 ◽  
Author(s):  
James H. Williams ◽  
Nagem Jr. ◽  
Yeung Raymond J. ◽  
Hubert K.
Keyword(s):  
Wave Propagation ◽  
Wave Mode ◽  
Scattering Matrices

Representations of 3-D Scattering Matrices

1991 ◽  
Author(s):  
Jerold R. Bottiger
Keyword(s):  
Scattering Matrices

On the Riccati Equations for the Scattering Matrices in Two Dimensions.

1995 ◽  
Author(s):  
Y. Chen ◽  
V. Rokhlin
Keyword(s):  
Riccati Equations ◽  
Two Dimensions ◽  
Scattering Matrices

scholarly journals Reducible Fermi Surface for Multi-layer Quantum Graphs Including Stacked Graphene

2021 ◽  
Author(s):  
Lee Fisher ◽  
Wei Li ◽  
Stephen P. Shipman
Keyword(s):  
Fermi Surface ◽  
Quantum Graphs

scholarly journals Average scattering entropy of quantum graphs

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Alison A. Silva ◽  
Fabiano M. Andrade ◽  
Dionisio Bazeia
Keyword(s):  
Quantum Graphs

scholarly journals Dirac particles on periodic quantum graphs

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
J. R. Yusupov ◽  
K. K. Sabirov ◽  
D. U. Matrasulov
Keyword(s):  
Quantum Graphs ◽  
Dirac Particles
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