- 99-389 Michael Aizenman, Jeffrey H. Schenker, Roland M. Friedrich, Dirk Hundertmark.
- Finite-volume Criteria for Anderson Localization
(120K, LaTeX 2e, 1 figure in epsf)
Oct 18, 99
(auto. generated ps),
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Abstract. For random Schr\"odinger operators, and a more general class of
operators with random potentials of `regular' probability distributions,
we present a family of constructive criteria for the localization
regime. A technically convenient characterization of localization is
rapid decay of the Green function's fractional moments.
In addition to explicit bounds, the constructive criteria
indicate that the exponential decay of the expectation values of such
functions may indeed characterize the entire regime of localization.
This has qualitative consequences -- since the fractional moment
condition is known to have other significant implications, such as
dynamical, as well as spectral, localization, and the exponential
decay of the expectation values of the spectral projection kernels.
In the converse direction,
the criteria also rule out fast power-law decay of the Green
function at mobility edges.