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arXiv · 0904.4829

Wegner-type bounds for a two-particle lattice model with a generic "rough" quasi-periodic potential

Martin Gaume
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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 $\Z^d$, $d\ge 1$ subject to a common external potential $V(x)$ which we assume quasi-periodic and depending on an auxiliary parameter. Such parametric families of ergodic deterministic potentials ("grand ensembles") have been introduced earlier in \cite{C07}, 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 grand ensembles. Using the approach proposed in \cite{CS08}, 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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Martin Gaume. 2009-05-28. Wegner-type bounds for a two-particle lattice model with a generic "rough" quasi-periodic potential. https://doi.org/10.1007/s11040-010-9075-x

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