Scattering theory on graphs

Details Scattering theory on graphs Scattering theory on graphs

2001-07-05

arxiv.org/abs/cond-mat/0107104v1

J. Phys. A: Math. Gen. 34 (2001) 10307-10326

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

21 pages, LaTeX, 10 eps figures

Scientific paper

10.1088/0305-4470/34/47/328

We consider the scattering theory for the Schr\"odinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.

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