Constructive Fractional-Moment Criteria for Localization in Random Operators

Details Constructive Fractional-Moment Criteria for Localization in Random Operators Constructive Fractional-Moment Criteria for Localization in Random Operators

2000-01-22

arxiv.org/abs/math-ph/0001035v1

Phys. A 279 (2000), 369

Physics

Mathematical Physics

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

Scientific paper

10.1016/S0378-4371(00)00012-1

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.

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