On reflectionless equi-transmitting matrices

• Autorzy: Kurasov P. , Ogik R. , Rauf A.

Identyfikatory

DOI

http://dx.doi.org/10.7494/OpMath.2014.34.3.483

• Języki publikacji: EN

Abstrakty

EN

Reflectionless equi-transmitting unitary matrices are studied in connection to matching conditions in quantum graphs. All possible such matrices of size 6 are described explicitly. It is shown that such matrices form 30 six-parameter families intersected along 12 five-parameter families closely connected to conference matrices.

Słowa kluczowe

EN

quantum graphs; vertex scattering matrix; equi-transmitting matrices

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2014
• Tom: Vol. 34, no. 3
• Strony: 483--501
• Opis fizyczny: Bibliogr. 11 poz., rys., tab.

Twórcy

autor

Kurasov P.

• Stockholm University Dept. of Mathematics 106 91 Stockholm, Sweden

autor

Ogik R.

• Stockholm University Dept. of Mathematics 106 91 Stockholm, Sweden

autor

Rauf A.

• Stockholm University Dept. of Mathematics 106 91 Stockholm, Sweden

Bibliografia

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• [3] T. Cheon, Reflectionless and equiscattering quantum graphs, Int. J. Adv. Systems and Measurements 5 (2012), 18–22.
• [4] M. Harmer, Hermitian symplectic geometry and extension theory, Journal of Physics. A. Mathematical and General 33 (2000), 9193–9203.
• [5] M. Harmer, Hermitian symplectic geometry and the factorization of the scattering matrix on graphs, Journal of Physics. A. Mathematical and General 33 (2000), 9015–9032.
• [6] J.M. Harrison, U. Smilansky, B. Winn, Quantum graphs where back-scattering is prohibited, J. Phys. A 40 (2007), 14181–14193.
• [7] R.B. Holmes, V.I. Paulsen, Optimal frames for erasures, Linear Algebra Appl. 377 (2004), 31–51.
• [8] P. Kurasov, M. Nowaczyk, Geometric properties of quantum graphs and vertex scattering matrices, Opuscula Math. 30 (2010) 3, 295–309.
• [9] O. Post, Spectral Analysis on Graph-like Spaces, Springer, 2010.
• [10] O. Turek, T. Cheon, Quantum graph vertices with permutation-symmetric scattering probabilities, Phys. Lett. A 375 (2011) 43, 3775–3780.
• [11] O. Turek, T. Cheon, Hermitian unitary matrices with modular permutation symmetry, arXiv:1104.0408.