Spatial and spectral multifractality of the local density of states at the mobility edge

Journal Article · Sat Mar 01 04:00:00 EST 1997 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.55.R7303· OSTI ID:530964

Huckestein, B; Klesse, R ^[1]

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1. Institut fuer Theoretische Physik, Universitaet zu Koeln, D-50937 Koeln (Germany)

We performed numerical calculations of the local density of states (LDOS) at disorder-induced localization-delocalization transitions. The LDOS defines a spatial measure for fixed energy and a spectral measure for fixed position. At the mobility edge both measures are multifractal, and their generalized dimensions D(q) and {tilde D}(q) are found to be proportional: D(q)=d{tilde D}(q), where d is the dimension of the system. This observation is consistent with the identification of the frequency-dependent length scale L{sub {omega}}{proportional_to}{omega}{sup {minus}1/d} as an effective system size. The calculations are performed for two- and three-dimensional dynamical network models with local time evolution operators. The energy dependence of the LDOS is obtained from the time evolution of the local wave-function amplitude of a wave packet, providing a numerically efficient way to obtain information about the multifractal exponents of the system. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 530964
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 12 Vol. 55; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CARRIER MOBILITY
CHARGE CARRIERS
ELECTRONIC STRUCTURE
ENERGY DEPENDENCE
ENERGY-LEVEL DENSITY
FRACTALS
FREQUENCY DEPENDENCE
SCALING LAWS
TIME DEPENDENCE
WAVE FUNCTIONS
localized states