Direct Scaling Analysis of localization in disordered systems. II. Multi-particle lattice systems

Abstract

We adapt a simplified version of the Multi-Scale Analysis presented in \cite{C11} to multi-particle tight-binding Anderson models. Combined with a recent eigenvalue concentration bound for multi-particle systems \cite{C10}, the new method leads to a simple proof of the multi-particle dynamical localization with more optimal decay bounds on eigenfunctions than in \cite{CS09b,AW09a,AW09b}, for a large class of strongly mixing random potentials. All earlier results required the random potential to be IID. We also extend the result on multi-particle localization to models with a rapidly decaying interaction.

References in corpus (5)

• Localization Bounds for Multiparticle Systems
• Multi-Particle Anderson Localisation: Induction on the Number of Particles
• Wegner bounds for a two-particle tight binding model
• A remark on charge transfer processes in multi-particle systems
• Direct Scaling Analysis of localization in disordered systems. I. Single-particle models

Cited by in corpus (4)

• On Many-Body Localization for Quantum Spin Chains
• Comprehensive proofs of localization in Anderson models with interaction. I. Two-particle localization estimates
• Lifshitz tails for the multi-particle continuous Anderson model
• On complete localization for the one-dimensional multi-particle Anderson-Bernoulli model with infinite range interaction