N-body localization for the Anderson model with strongly mixing\n correlated random potentials

2017/02/22 by Trésor Ekanga, Ekanga, Trésor · 1 citation
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1702.07010

openalex publication_date 2017/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work establishes the Anderson localization in both the spectral\nexponential and the strong dynamical localization for the multi-particle\nAnderson tight-binding model with correlated but strongly mixing random\nexternal potential. The results are obtained near the lower edge of the\nspectrum of the multi-particle Hamiltonian. In particular, the exponential\ndecay of the eigenfunctions is proved in the max-norm and the dynamical\nlocalization in the Hilbert-Schmidt norm. The proofs need the conditional\nprobability distribution function of the random external stochastic processes\nto obey the uniform log-H "older continuity condition.\n

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