Localization for Random Operators with Non-monotone Potentials with Exponentially Decaying Correlations
作者： Helge Krüger
DOI: 10.1007/S00023-011-0130-3
关键词: Schrödinger's cat 、 Statistical physics 、 Mathematical analysis 、 Exponential growth 、 Anderson localization 、 Eigenfunction 、 Non monotone 、 Single site 、 Mathematics 、 Sign (mathematics)
摘要: I consider random Schrodinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, prove Anderson localization both in the sense of eigenfunctions and dynamical localization. Furthermore, results imply a Wegner-type estimate strong enough use classical forms multi-scale analysis.
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sci-hub.se 参考文章(52)
J. Bourgain, S. Jitomirskaya, Anderson localization for the band model Springer Berlin Heidelberg. pp. 67- 79 ,(2000) , 10.1007/BFB0107208
Jean Bourgain, Green's Function Estimates for Lattice Schrödinger Operators and Applications. ,(2004)
Peter Stollmann, Caught by Disorder: Bound States in Random Media ,(2001)
Günter Stolz, An Introduction to the Mathematics of Anderson Localization arXiv: Mathematical Physics. ,(2011)
François Germinet, Abel Klein, A characterization of the Anderson metal-insulator transport transition Duke Mathematical Journal. ,vol. 124, pp. 309- 350 ,(2004) , 10.1215/S0012-7094-04-12423-6
Henrique von Dreifus, Abel Klein, A New Proof of Localization in the Anderson Tight Binding Model Communications in Mathematical Physics. ,vol. 124, pp. 285- 299 ,(1989) , 10.1007/BF01219198
Abel Klein, François Germinet, Peter Hislop, Localization for Schrödinger operators with Poisson random potential Journal of the European Mathematical Society. ,vol. 9, pp. 577- 607 ,(2007) , 10.4171/JEMS/89
Jean Bourgain, Carlos E. Kenig, On localization in the continuous Anderson-Bernoulli model in higher dimension Inventiones Mathematicae. ,vol. 161, pp. 389- 426 ,(2005) , 10.1007/S00222-004-0435-7
Ivan Veselić, Wegner Estimate for Discrete Alloy-type Models Annales Henri Poincaré. ,vol. 11, pp. 991- 1005 ,(2010) , 10.1007/S00023-010-0052-5