M ar 2 00 2 Scattering theory on graphs ( 2 ) : the Friedel sum rule Christophe Texier 22 nd February 2002


We consider the Friedel sum rule in the context of the scattering theory for the Schrödinger operator −D2 x + V (x) on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples of graphs where the state counting method given by the Friedel sum rule is not working. The reason for… (More)


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