Abstract
We consider a quantum two-particle system on a lattice \({\mathbb{Z}^d}\) with interaction and in presence of an IID external potential. We establish Wegner-type estimates for such a model. The main tool used is Stollmann’s lemma.
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Chulaevsky, V.: A simple extension of Stollmann’ lemma for correlated potentials. Preprint, Université de Reims, April 2006.; http://arXiv.org/abs/0705:2873, 2007
Chulaevsky, V., Suhov, Y.: Anderson localisation for an interacting two-particle quantum system on \({{\mathbb Z}}\). http://arXiv.org/abs/0705:0657, 2007
von Dreifus H., Klein A.: A new proof of Localization in the Anderson Tight Binding Model. Commun. Math. Phys. 124, 285–299 (1989)
Fröhlich J., Martinelli F., Scoppola E., Spencer T.: A constructive proof of localization in Anderson tight binding model. Commun. Math. Phys. 101, 21–46 (1985)
Kirsch, W.: A Wegner estimate for multi-particle random Hamiltonians. http://arXiv.org/abs/0704:2664, 2007
Stollmann P.: Wegner estimates and localization for continuous Anderson models with some singular distributions. Arch. Math. 75, 307–311 (2000)
Stollmann, P.: Caught by disorder. Basel-Boston: Birkhäuser, 2001
Wegner F.: Bounds on the density of states in disordered systems. Z. Phys. B. Condensed Matter 44, 9–15 (1981)
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Communicated by B. Simon
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Chulaevsky, V., Suhov, Y. Wegner Bounds for a Two-Particle Tight Binding Model. Commun. Math. Phys. 283, 479–489 (2008). https://doi.org/10.1007/s00220-008-0508-3
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DOI: https://doi.org/10.1007/s00220-008-0508-3