TY - JOUR
T1 - Constructive fractional-moment criteria for localization in random operators
AU - Aizenman, Michael
AU - Schenker, Jeffrey H.
AU - Friedrich, Roland M.
AU - Hundertmark, Dirk
PY - 2000/5/1
Y1 - 2000/5/1
N2 - 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.
AB - 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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U2 - 10.1016/S0378-4371(00)00012-1
DO - 10.1016/S0378-4371(00)00012-1
M3 - Article
AN - SCOPUS:0033727833
SN - 0378-4371
VL - 279
SP - 369
EP - 377
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1
ER -