An Isaac Newton Institute Workshop

Graph Models of Mesoscopic Systems, Wave-Guides and Nano-Structures

On the skeleton method

Author: Pierre Duclos (Toulon)

Abstract

In the spectral analysis of few one dimensional quantum particles interacting through delta potentials it is well known that one can recast the problem into the spectral analysis of an integral operator (the skeleton) living on the submanifold which supports the delta interactions. We shall present several tools which allow direct insights into the spectral structure of this skeleton. Application to effective models of excitons in nanotubes as well as some nets of quantum wires will be given. This is a work in progress with H. Cornean and B. Ricaud, see e.g.

Three quantum charged particles interacting through delta potentials}, Few-Body Systems 38(2-4), 125-131, 2006, ArXiv math-ph/0604003