The Generalized Star Product and the Factorization of Scattering Matrices on Graphs

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dc.creatorKostrykin, Vadim
dc.creatorSchrader, Robert
dc.date2000-08-15
dc.date.accessioned2026-07-25T22:13:31Z
dc.descriptionIn this article we continue our analysis of Schrödinger operators on arbitrary graphs given as certain Laplace operators. In the present paper we give the proof of the composition rule for the scattering matrices. This composition rule gives the scattering matrix of a graph as a generalized star product of the scattering matrices corresponding to its subgraphs. We perform a detailed analysis of the generalized star product for arbitrary unitary matrices. The relation to the theory of transfer matrices is also discussed.
dc.identifierhttps://arxiv.org/abs/math-ph/0008022
dc.identifierhttp://arxiv.org/abs/math-ph/0008022
dc.identifierJ. Math. Phys. Vol. 42 (2001), 1563 - 1598
dc.identifierdoi:10.1063/1.1354641
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/87053
dc.subjectMathematical Physics
dc.subject34B45; 34L40; 47A40; 81U20
dc.titleThe Generalized Star Product and the Factorization of Scattering Matrices on Graphs
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