Publication : t10/271

Anderson Model on Bethe Lattices: Density of States, Localization Properties and Isolated Eigenvalue

Biroli G. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Semerjian G. (LPTENS, CNRS UMR 8549, associée à Univ. P. et M. Curie Paris VI, 24 rue Lhomond, F-75005 Paris, France)
Tarzia M. (LPTMC-UPMC, UMR CNRS 7600, 4 place Jussieu, F-75252 Paris Cedex 05, France)
Abstract:
We revisit the Anderson localization problem on Bethe lattices, putting in contact various aspects which have been previously only discussed separately. For the case of connectivity 3 we compute by the cavity method the density of states and the evolution of the mobility edge with disorder. Furthermore, we show that below a certain critical value of the disorder the smallest eigenvalue remains delocalized and separated by all the others (localized) ones by a gap. We also study the evolution of the mobility edge at the center of the band with the connectivity, and discuss the large connectivity limit.
Année de publication : 2010
Revue : Prog. Theor. Phys. (Suppl. ) 184 187-199 (2010)
Conférence - Communication : 17th Yukawa International Seminar 2009 (YKIS2009) "Frontiers in Nonequilibrium Physics – Fundamental Theory, Glassy & Granular Materials, and Computational Physics –" ; Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kyoto, Japan ; 2009-07-21 / 2009-08-21
DOI : 10.1143/PTPS.184.187
Preprint : arXiv:1005.0342v2
Langue : Anglais
NB : 13 pages, 4 figures

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