 00308 Peter Kuchment and Hongbiao Zeng
 Convergence of spectra of mesoscopic systems collapsing onto a graph
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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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