Edge Switching Transformations of Quantum Graphs

• Authors: M. Aizenman , H. Schanz , U. Smilansky , S. Warzel
• Languages of publication: EN

Abstracts

EN

Discussed here are the effects of basics graph transformations on the spectra of associated quantum graphs. In particular it is shown that under an edge switch the spectrum of the transformed Schrödinger operator is interlaced with that of the original one. By implication, under edge swap the spectra before and after the transformation, denoted by {Eₙ}^{∞}ₙ₌₁ and {Ẽₙ}^{∞}ₙ₌₁ correspondingly, are level-2 interlaced, so that Eₙ-₂ ≤ Ẽₙ ≤ Eₙ₊₂. The proofs are guided by considerations of the quantum graphs' discrete analogs.

Keywords

EN

05.45.Mt; 02.10.Ox

Discipline

• 02.10.Ox: Combinatorics; graph theory
• 05.45.Mt: Quantum chaos; semiclassical methods

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2017
• Volume: 132
• Issue: 6
• Pages: 1699-1703

Dates

published

2017-12

Contributors

author

M. Aizenman

• Departments of Physics and Mathematics, Princeton University, Princeton NJ 08540, USA

author

H. Schanz

• Institute of Mechanical Engineering, University of Applied Sciences Magdeburg-Stendal, D-39114 Magdeburg, Germany

author

U. Smilansky

• Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel

author

S. Warzel

• Zentrum Mathematik, TU München, Boltzmannstr. 3, 85747 Garching, Germany

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Identifiers

DOI

10.12693/APhysPolA.132.1699