Scattering theory on metric graphs
In the field of mesoscopic physics, many interesting effects have been studied on systems that can be modelized by a graph: a network of one dimensional wires connected at nodes and on which may live a potential. These simple models are often sufficient to capture the physics of interest, like interference effects. A particularly fruitful approach to describe many properties of phase coherent systems connected to contacts through which current can be injected (transport, noise,…) is the scattering approach of Landauer and Büttiker. At the core of this approach is the scattering matrix. In the following works, it is explained how the scattering matrix of any graph (network) can be computed very systematically. Several properties of the scattering are studied, like its precise relation with local information inside the graph.
- Christophe Texier and Gilles Montambaux,
Scattering theory on graphs
J. Phys. A: Math. Gen. 34, (2001), 10307-10326.
- Christophe Texier,
Scattering theory on graphs (2) : the Friedel sum rule
J. Phys. A: Math. Gen. 35, (2002), 3389-3407.
- Christophe Texier and Markus Büttiker,
Local Friedel sum rule on graphs
Phys. Rev. B 67, (2003), 245410.
- Christophe Texier and Pascal Degiovanni,
Charge and currents distribution in graphs
J. Phys. A: Math. Gen. 36, (2003), 12425-12452.