00-308 Peter Kuchment and Hongbiao Zeng
Convergence of spectra of mesoscopic systems collapsing onto a graph (644K, LATeX2e with one TIF figure) Jul 29, 00
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Abstract. Let $M$ be a finite graph in the plane and $M^{\,\varepsilon }$ be a domain that looks like the $\varepsilon$-fattened graph $M$ (exact conditions on the domain are given). It is shown that the spectrum of the Neumann Laplacian on $M^{\,\varepsilon }$ converges when $\varepsilon \rightarrow 0$ to the spectrum of an ODE problem on $M$. Presence of an electromagnetic field is also allowed. Considerations of this kind arise naturally in mesoscopic physics and other areas of physics and chemistry. The results of the paper extend the ones previously obtained by J. Rubinstein and M. Schatzman.

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