TY - JOUR
T1 - Absolutely Continuous Spectrum for Quantum Trees
AU - Anantharaman, Nalini
AU - Ingremeau, Maxime
AU - Sabri, Mostafa
AU - Winn, Brian
N1 - Publisher Copyright:
© 2021, The Author(s).
PY - 2021/4
Y1 - 2021/4
N2 - 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.
AB - 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.
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U2 - 10.1007/s00220-021-03994-3
DO - 10.1007/s00220-021-03994-3
M3 - Article
AN - SCOPUS:85101133615
SN - 0010-3616
VL - 383
SP - 537
EP - 594
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 1
ER -