Abstract
We consider a sequence of finite quantum graphs with few loops, so that they converge, in the sense of Benjamini-Schramm, to a random infinite quantum tree. We assume these quantum trees are spectrally delocalized in some interval I, in the sense that their spectrum in I is purely absolutely continuous and their Green's functions are well controlled near the real axis. We furthermore suppose that the underlying sequence of discrete graphs is expanding. We deduce a quantum ergodicity result, showing that the eigenfunctions with eigenvalues lying in I are spatially delocalized.
Original language | English (US) |
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Pages (from-to) | 28-98 |
Number of pages | 71 |
Journal | Journal des Mathematiques Pures et Appliquees |
Volume | 151 |
DOIs | |
State | Published - Jul 2021 |
Keywords
- Delocalization
- Quantum ergodicity
- Quantum graphs
- Trees
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics