Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method

Abstract

A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators we establish a finite-volume criterion which implies that above mentioned the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e. g. at spectral boundaries which satisfy 'Lifshitz tail estimates' on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials.

29 pages, 1 figure, to appear in AHP

References in corpus (3)

• Correlations Estimates in the Lattice Anderson Model
• On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials
• Lipschitz-continuity of the integrated density of states for Gaussian random potentials

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