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Wegner-type Bounds for a Two-particle Lattice Model with a Generic “Rough” Quasi-periodic Potential

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Abstract

In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles on the lattice ℤd, d ≥ 1, subject to a common external potential V(x) which we assume quasi-periodic and depending on auxiliary parameters. Such parametric families of ergodic deterministic potentials (“grands ensembles”) have been introduced earlier in Chulaevsky (2007), in the framework of single-particle lattice systems, where it was proved that a non-uniform analog of the Wegner bound holds true for a class of quasi-periodic grands ensembles. Using the approach proposed in Chulaevsky and Suhov (Commun Math Phys 283(2):479–489, 2008), we establish volume-dependent Wegner-type bounds for a class of quasi-periodic two-particle lattice systems with a non-random short-range interaction.

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  1. Institut de Mathématiques de Jussieu, Université Paris Diderot, Site Chevaleret, case 7012, 75205, Paris Cedex 13, France

    Martin Gaume

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  1. Martin Gaume
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Gaume, M. Wegner-type Bounds for a Two-particle Lattice Model with a Generic “Rough” Quasi-periodic Potential. Math Phys Anal Geom 13, 205–217 (2010). https://doi.org/10.1007/s11040-010-9075-x

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