Optimal Wegner estimate and the density of states for N-body, interacting Schrodinger operators with random potentials

Abstract

We prove an optimal one-volume Wegner estimate for interacting systems of $N$ quantum particles moving in the presence of random potentials. The proof is based on the scale-free unique continuation principle recently developed for the 1-body problem by Rojas-Molina and Veselic \cite{RM-V1} and extended to spectral projectors by Klein \cite{klein1}. These results extend of our previous results in \cite{CHK:2003,CHK:2007}. We also prove a two-volume Wegner estimate as introduced in \cite{chulaevsky-suhov1}. The random potentials are generalized Anderson-type potentials in each variable with minimal conditions on the single-site potential aside from positivity. Under additional conditions, we prove the Lipschitz continuity of the integrated density of states (IDS) This implies the existence and local finiteness of the density of states. We also apply these techniques to interacting $N$-particle Schrödinger operators with Delone-Anderson type random external potentials.

References in corpus (5)

• A comprehensive proof of localization for continuous Anderson models with singular random potentials
• Wegner bounds for a two-particle tight binding model
• The bootstrap multiscale analysis for the multi-particle Anderson model
• A Wegner estimate for multi-particle random Hamiltonians
• Unique continuation principle for spectral projections of Schr\" odinger operators and optimal Wegner estimates for non-ergodic random Schr\" odinger operators

Cited by in corpus (2)

• Wegner bounds for N-body interacting Bernoulli-Anderson models in one dimension
• Wegner bounds for one-dimensional multi-particle Bernoulli-Anderson models in the continuum