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arXiv · 0906.2825

Quantum scattering theory on graphs with tails

Martin Varbanov·Todd A. Brun
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Abstract

We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved as well as some other of its properties such as its transformation under time reversal. A spectral decomposition of the identity for the Hamiltonian of the graph is derived using its eigenvectors. We derive formulas for the S-matrix of a graph under certain operation such as cutting a tail, attaching a tail or connecting two tails to form an edge.

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Martin Varbanov, Todd A. Brun. 2009-06-15. Quantum scattering theory on graphs with tails. https://doi.org/10.1103/physreva.80.052330

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