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

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.