Constructive Fractional-Moment Criteria for Localization in Random Operators

M. Aizenman, J. H. Schenker, R. M. Friedrich, D. Hundertmark

Published 2000-01-22Version 1

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.