Scattering solutions in a network of thin fibers: small diameter asymptotics

Details Scattering solutions in a network of thin fibers: small diameter asymptotics Scattering solutions in a network of thin fibers: small diameter asymptotics

2006-09-08

arxiv.org/abs/math-ph/0609021v2

Physics

Mathematical Physics

Scientific paper

10.1007/s00220-007-0220-8

Small diameter asymptotics is obtained for scattering solutions in a network of thin fibers. The asymptotics is expressed in terms of solutions of related problems on the limiting quantum graph. We calculate the Lagrangian gluing conditions at vertices for the problems on the limiting graph. If the frequency of the incident wave is above the bottom of the absolutely continuous spectrum, the gluing conditions are formulated in terms of the scattering data for each individual junction of the network.

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