Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder

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dc.creatorAizenman, Michael
dc.creatorSims, Robert
dc.creatorWarzel, Simone
dc.date2005-04-12
dc.date2005-06-05
dc.date.accessioned2026-07-07T06:30:08Z
dc.date.available2026-07-07T06:30:08Z
dc.descriptionWe consider the Laplacian on a rooted metric tree graph with branching number $ K \geq 2 $ and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generalization of the Weyl-Titchmarsh function to trees. The proof of the main result rests on upper bounds on the range of fluctuations of this quantity in the limit of weak disorder.
dc.identifierhttps://arxiv.org/abs/math-ph/0504039
dc.identifierhttp://arxiv.org/abs/math-ph/0504039
dc.identifierCommun. Math. Phys. 264 (2006) 371 - 389
dc.identifierdoi:10.1007/s00220-005-1468-5
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98268
dc.subjectMathematical Physics
dc.subjectDisordered Systems and Neural Networks
dc.subjectSpectral Theory
dc.titleAbsolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder
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