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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 487
The Generalized Star Product and the Factorization of Scattering Matrices on Graphs V. Kostrykin and R. Schrader
In 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.
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