scholarly journals Quantum ergodicity for large equilateral quantum graphs

2019 ◽  
Vol 101 (1) ◽  
pp. 82-109
Author(s):  
Maxime Ingremeau ◽  
Mostafa Sabri ◽  
Brian Winn
Keyword(s):  
Quantum Graphs ◽  
Quantum Ergodicity

scholarly journals Quantum Ergodicity for Quantum Graphs without Back-Scattering

2015 ◽  
Vol 17 (6) ◽  
pp. 1353-1382 ◽  
Author(s):  
Matthew Brammall ◽  
B. Winn
Keyword(s):  
Quantum Graphs ◽  
Quantum Ergodicity ◽  
Back Scattering

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

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.

scholarly journals The first eigenvalue of the $$p-$$ p - Laplacian on quantum graphs

2016 ◽  
Vol 6 (4) ◽  
pp. 365-391 ◽  
Author(s):  
Leandro M. Del Pezzo ◽  
Julio D. Rossi
Keyword(s):  
First Eigenvalue ◽  
Quantum Graphs ◽  
The First Eigenvalue

scholarly journals Quantum graphs: Self-adjoint, and yet exhibiting a nontrivial PT-symmetry

2021 ◽  
Vol 416 ◽  
pp. 127669
Author(s):  
Pavel Exner ◽  
Miloš Tater
Keyword(s):  
Pt Symmetry ◽  
Quantum Graphs
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