Persistence under Weak Disorder of AC Spectra of Quasi-Periodic Schroedinger operators on Trees Graphs

Details Persistence under Weak Disorder of AC Spectra of Quasi-Periodic Schroedinger operators on Trees Graphs Persistence under Weak Disorder of AC Spectra of Quasi-Periodic Schroedinger operators on Trees Graphs

2005-04-29

arxiv.org/abs/math-ph/0504084v3

Moscow Math. Jour., vol. 5, no. 3 (2005), 499-506

Physics

Mathematical Physics

Dedicated to Ya. Sinai on the occasion of his seventieth birthday

Scientific paper

We consider radial tree extensions of one-dimensional quasi-periodic
Schroedinger operators and establish the stability of their absolutely
continuous spectra under weak but extensive perturbations by a random
potential. The sufficiency criterion for that is the existence of Bloch-Floquet
states for the one dimensional operator corresponding to the radial problem.

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