Bootstrap multiscale analysis and localization for multi-particle continuous Anderson Hamiltonians

Abstract

We extend the bootstrap multiscale analysis developed by Germinet and Klein to the multi-particle continuous Anderson Hamiltonian, obtaining Anderson localization with finite multiplicity of eigenvalues, decay of eigenfunction correlations, and a strong form of dynamical localization. We do not require a covering condition. The initial step for this multiscale analysis, required to hold for energies in a nontrivial interval at the bottom of the spectrum, is verified for multi-particle continuous Anderson Hamiltonians. We also extend the unique continuation principle for spectral projections of Schrödinger operators to arbitrary rectangles, and use it to prove Wegner estimates for multi-particle continuous Anderson Hamiltonians without the requirement of a covering condition.