# Recovering quantum graphs from their Bloch spectrum

Ralf Rueckriemen^{[1]}

- [1] Dartmouth College, Kemeny Hall, Hanover, 03755 NH, USA

Annales de l’institut Fourier (2013)

- Volume: 63, Issue: 3, page 1149-1176
- ISSN: 0373-0956

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topRueckriemen, Ralf. "Recovering quantum graphs from their Bloch spectrum." Annales de l’institut Fourier 63.3 (2013): 1149-1176. <http://eudml.org/doc/275536>.

@article{Rueckriemen2013,

abstract = {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 Schrödinger 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.},

affiliation = {Dartmouth College, Kemeny Hall, Hanover, 03755 NH, USA},

author = {Rueckriemen, Ralf},

journal = {Annales de l’institut Fourier},

keywords = {quantum graphs; Schrödinger operators; spectrum; inverse spectral problem; quantum graph; Bloch spectrum},

language = {eng},

number = {3},

pages = {1149-1176},

publisher = {Association des Annales de l’institut Fourier},

title = {Recovering quantum graphs from their Bloch spectrum},

url = {http://eudml.org/doc/275536},

volume = {63},

year = {2013},

}

TY - JOUR

AU - Rueckriemen, Ralf

TI - Recovering quantum graphs from their Bloch spectrum

JO - Annales de l’institut Fourier

PY - 2013

PB - Association des Annales de l’institut Fourier

VL - 63

IS - 3

SP - 1149

EP - 1176

AB - 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 Schrödinger 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.

LA - eng

KW - quantum graphs; Schrödinger operators; spectrum; inverse spectral problem; quantum graph; Bloch spectrum

UR - http://eudml.org/doc/275536

ER -

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