Nodal domains, spectral minimal partitions, and their relation to Aharonov-Bohm operators

2017/11/02 by Virginie Bonnaillie‐Noël, Bernard Helffer, Bonnaillie-Noël, Virginie +3
Mathematics · Physics and Astronomy · Materials Science · #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1711.01174

Abstract

This survey is a short version of a chapter written by the first two authors in the book [A. Henrot, editor. Shape optimization and spectral theory. Berlin: De Gruyter, 2017] (where more details and references are given) but we have decided here to put more emphasis on the role of the Aharonov-Bohm operators which appear to be a useful tool coming from physics for understanding a problem motivated either by spectral geometry or dynamics of population. Similar questions appear also in Bose-Einstein theory. Finally some open problems which might be of interest are mentioned.

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