RECOVERING QUANTUM GRAPHS FROM THEIR BLOCH SPECTRUM

被引：0

作者：

Rueckriemen, Ralf ^{[1
]}

机构：

[1] Dartmouth Coll, Hanover, NH 03755 USA

来源：

ANNALES DE L INSTITUT FOURIER | 2013年 / 63卷 / 03期

关键词：

quantum graphs; Schrodinger operators; spectrum; inverse spectral problem; ONE HEAR; SHAPE; TORI;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define the Bloch spectrum of a quantum graph to be the map that assigns to each element in the deRham cohomology the spectrum of an associated magnetic Schrodinger operator. We show that the Bloch spectrum determines the Albanese torus, the block structure and the planarity of the graph. It determines a geometric dual of a planar graph. This enables us to show that the Bloch spectrum indentifies and completely determines planar 3-connected quantum graphs.

引用

页码：1149 / 1176

页数：28

共 16 条

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