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We performed numerical calculations of the local density of states (LDOS) atdisorder induced localization-delocalization transitions. The LDOS defines aspatial measure for fixed energy and a spectral measure for fixed position. Atthe mobility edge both measures are multifractal and their generalizeddimensions $D(q)$ and $\tilde{D}(q)$ are found to be proportional:$D(q)=d\tilde{D}(q)$, where $d$ is the dimension of the system. Thisobservation is consistent with the identification of the frequency-dependentlength scale $L_\omega \propto \omega^{-1/d}$ as an effective system size. Thecalculations are performed for two- and three-dimensional dynamical networkmodels with local time evolution operators. The energy dependence of the LDOSis obtained from the time evolution of the local wavefunction amplitude of awave packet, providing a numerically efficient way to obtain information aboutthe multifractal exponents of the system.Comment: updated 2 references, no further change

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