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Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder | | Michael Aizenman
; Robert Sims
; Simone Warzel
; | | Date: |
12 Apr 2005 | | Subject: | Mathematical Physics; Spectral Theory; Disordered Systems and Neural Networks | math-ph cond-mat.dis-nn math.MP math.SP | | Abstract: | We 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. | | Source: | arXiv, math-ph/0504039 | | Services: | Forum | Review | PDF | Favorites | |
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