Communication: Probing anomalous diffusion in frequency space.

Anomalous diffusion processes are usually detected by analyzing the time-dependent mean square displacement of the diffusing particles. The latter evolves asymptotically as W(t) ∼ 2Dαt(α), where Dα is the fractional diffusion constant and 0 < α < 2. In this article we show that both Dα and α can also be extracted from the low-frequency Fourier spectrum of the corresponding velocity autocorrelation function. This offers a simple method for the interpretation of quasielastic neutron scattering spectra from complex (bio)molecular systems, in which subdiffusive transport is frequently encountered. The approach is illustrated and validated by analyzing molecular dynamics simulations of molecular diffusion in a lipid POPC bilayer.

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