Constructive Fractional-Moment Criteria for Localization in Random Operators

Abstract

We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.

Announcement and summary of results whose proofs are given elsewhere. LaTex (10 pages), uses Elsevier "elsart" files (attached)

References in corpus (1)

• Charge Deficiency, Charge Transport and Comparison of Dimensions

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