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Exterior-Interior Duality for Discrete Graphs
The Exterior-Interior duality expresses a deep connection between the Laplace
spectrum in bounded and connected domains in , and the scattering
matrices in the exterior of the domains. Here, this link is extended to the
study of the spectrum of the discrete Laplacian on finite graphs. For this
purpose, two methods are devised for associating scattering matrices to the
graphs. The Exterior -Interior duality is derived for both methods.Comment: 15 pages 1 figur
Inelastic electron-nucleus scattering and scaling at high inelasticity
Highly inelastic electron scattering is analyzed within the context of the
unified relativistic approach previously considered in the case of quasielastic
kinematics. Inelastic relativistic Fermi gas modeling that includes the
complete inelastic spectrum - resonant, non-resonant and Deep Inelastic
Scattering - is elaborated and compared with experimental data. A
phenomenological extension of the model based on direct fits to data is also
introduced. Within both models, cross sections and response functions are
evaluated and binding energy effects are analyzed. Finally, an investigation of
the second-kind scaling behavior is also presented.Comment: 39 pages, 13 figures; formalism extended and slightly reorganized,
conclusions extended; to appear in Phys. Rev.
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