2008
DOI: 10.1007/s00220-008-0508-3
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Wegner Bounds for a Two-Particle Tight Binding Model

Abstract: We consider a quantum two-particle system on a lattice Z d with interaction and in presence of an IID external potential. We establish Wegner-typer estimates for such a model. The main tool used is Stollmann's lemma.

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Cited by 39 publications
(77 citation statements)
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“…Quite recently, Anderson-type models for a fixed number N of interacting electrons in a random background have been shown to have localization properties. Chulaevsky and Suhov [15,16] have done this by an extension of multiscale analysis, while [7] povides similar results based on the fractional moments approach.…”
Section: Open Problems and Directions For Future Workmentioning
confidence: 85%
“…Quite recently, Anderson-type models for a fixed number N of interacting electrons in a random background have been shown to have localization properties. Chulaevsky and Suhov [15,16] have done this by an extension of multiscale analysis, while [7] povides similar results based on the fractional moments approach.…”
Section: Open Problems and Directions For Future Workmentioning
confidence: 85%
“…, η n }. Therefore, the conditional probability distribution of ξ n given F η coincides with the unconditional one, N (0, n −1 ), thus ξ n has bounded conditional density 2) and for any interval I ⊂ R of length |I|, we have…”
Section: Formulation Of the Problemmentioning
confidence: 91%
“…Let F (2) be the sigma-algebra generated by X (2) . The conditional distribution of X given X (2) differs from that of X (1) (i.e., from the measure µ 1 ) only by a shift (nonrandom, conditional on F (2) ). Thus we have…”
Section: Corollary 2 ((V3)) the Condition (V3) Implies (Rcm)mentioning
confidence: 99%
“…As was commented on in [7] and [9] (and earlier in [12], [13], [14] and [8] in the context of tight-binding models), the principal difficulty encountered while attempting to extend the SPMSA to the MPMSA is that for N > 1 the random field…”
Section: 2mentioning
confidence: 99%