Convergence of spectra of mesoscopic systems collapsing onto a graph
Kuchment, Peter Zeng, Hongbiao
Kuchment, Peter
Zeng, Hongbiao
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2001-06-15
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Article
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Mesoscopic system,Schrödinger operator,Spectrum
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Citation
Peter Kuchment, Hongbiao Zeng, Convergence of Spectra of Mesoscopic Systems Collapsing onto a Graph, Journal of Mathematical Analysis and Applications, Volume 258, Issue 2, 2001, Pages 671-700, ISSN 0022-247X, https://doi.org/10.1006/jmaa.2000.7415.
Abstract
Let M be a finite graph in the plane and let Mε be a domain that looks like the ε-fattened graph M (exact conditions on the domain are given). It is shown that the spectrum of the Neumann Laplacian on Mε converges when ε→0 to the spectrum of an ODE problem on M. The 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. © 2001 Academic Press.
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This is an open access article under the CC BY license.
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Academic Press Inc.
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Journal of Mathematical Analysis and Applications
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0022247X