Convergence of Spectra of Mesoscopic Systems Collapsing onto a Graph
Convergence of Spectra of Mesoscopic Systems Collapsing onto a Graph
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介观系统光谱收敛到图上
DOI：
10.1006/jmaa.2000.7415
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发表时间：
2001
影响因子：
1.3
通讯作者：
Hongbiao Zeng
中科院分区：
文献类型：
--
作者：
P. Kuchment;Hongbiao Zeng
设M是平面上的有限图，Me是一个类似e-胖图M的区域（给出了该区域的精确条件）。证明了当e → 0时，M上NeumannLaplacian的谱收敛于M上一个常微分方程的谱.电磁场的存在也是允许的。这类考虑自然出现在介观物理学和其他物理学和化学领域。本文的结果推广了J. Rubinstein和M.沙兹曼。
Abstract Let M be a finite graph in the plane and let Me be a domain that looks like the e-fattened graph M (exact conditions on the domain are given). It is shown that the spectrum of the Neumann Laplacian on Me converges when e → 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.