Absolutely Continuous Spectrum for Quantum Trees

Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri, Brian Winn

Research output: Contribution to journalArticlepeer-review


We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum consists of bands of purely absolutely continuous spectrum, along with a discrete set of eigenvalues. Afterwards, we study random perturbations of such trees, at the level of edge length and coupling, and prove the stability of pure AC spectrum, along with resolvent estimates.

Original languageEnglish (US)
Pages (from-to)537-594
Number of pages58
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Apr 2021

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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