Nodal domains, spectral minimal partitions, and their relation to Aharonov-Bohm operators
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.
arXiv commentarXiv admin note: substantial text overlap with arXiv:1506.07249
References in corpus (12)
- Nodal domains statistics - a criterion for quantum chaos
- Faber-Krahn inequalities in sharp quantitative form
- Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions
- Nodal domains of Maass forms I
- Nodal portraits of quantum billiards: Domains, lines, and statistics
- On the connection between the number of nodal domains on quantum graphs and the stability of graph partitions
- Liouville theorems and -dimensional symmetry for solutions of an elliptic system modelling phase separation
- On the eigenvalues of Aharonov-Bohm operators with varying poles
- Remarks on the boundary set of spectral equipartitions
- Pleijel's theorem for Schrödinger operators with radial potentials
- The Honeycomb Problem on the Sphere
- Optimal partitions for the sum and the maximum of eigenvalues