Abstract
We adapt the method of direct scaling analysis developed earlier for single-particle Anderson models, to the fermionic multiparticle models with finite or infinite interaction on graphs. Combined with a recent eigenvalue concentration bound for multiparticle systems, the new method leads to a simpler proof of the multiparticle dynamical localization with optimal decay bounds in a natural distance in the multiparticle configuration space, for a large class of strongly mixing random external potentials. Earlier results required the random potential to be IID.
Highlights
We adapt the method of direct scaling analysis developed earlier for single-particle Anderson models, to the fermionic multiparticle models with finite or infinite interaction on graphs
Combined with a recent eigenvalue concentration bound for multiparticle systems, the new method leads to a simpler proof of the multiparticle dynamical localization with optimal decay bounds in a natural distance in the multiparticle configuration space, for a large class of strongly mixing random external potentials
Analysis of localization phenomena in multiparticle quantum systems with nontrivial interaction in a random environment is a relatively new direction in the Anderson localization theory, where during almost half a century, since the seminal paper by Anderson [1], most efforts were concentrated on the study of disordered systems in the single-particle approximation, that is, without interparticle interaction
Summary
The LHS of (20) is a conditional probability, a random variable, so (20) holds P-a.s. To formulate the assumption, introduce the following notation: given a subset Λ ⊂ Z, we denote by FVΛ the sigma-algebra generated by the values of the random potential {V(x; ω), x ∈ Λ}. Conventional EVC bounds seem so far insufficient for the proof of the exponential decay of eigenfunctions and EF correlators with respect to a norm in the configuration space of N-particle systems, starting from N = 3 For this reason, we proposed earlier [20] a new method for comparing spectra of two strongly correlated multiparticle subsystems and improved the EVC estimate from [4]. We will prove the multiparticle localization first under the strongest assumption (U0) (leading to a simpler proof), to illustrate the general structure of the DSA procedure, and extend the proof to the infiniterange interactions satisfying (U1)
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