Stationary spectra for p <  = 100p₀ for different fractional dimension α considering Lévy flights. On the left, the resulting energy spectra are shown. The dots are simulation results, and lines indicate the slopes fitted to the range p = (10, 100)p₀. The fitted slopes are shown in comparison to the slopes for Lévy walks in the right panel, depending on the fractional dimension α and (pseudo) mean-square displacement. The fitted values for the Lévy flights are (with decreasing fractional dimension): s = −2.012 + −0.004,  s = −1.934 ± 0.003,  s = −1.844 ± 0.005 s = −1.764 ± 0.005,  s = −1.659 ± 0.013,  s = −1.576 ± 0.012.