SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 56: Brownian Motion and Anomalous Diffusion

DY 56.10: Vortrag

Freitag, 31. März 2023, 12:15–12:30, ZEU 160

Universal hyper-scaling relations, power-law tails, and data analysis for strong anomalous diffusion — •Jürgen Vollmer¹, Lamberto Rondoni², Claudio Giberti³, and Carlos Mejía-Monasterio⁴ — ¹Inst. Theor. Physik, Univ. Leipzig, 04103 Leipzig, Germany — ²Dept. Math. Sc., Politecnico di Torino, 10129 Torino, Italy — ³Dept. Scienze e Metodi dell Ingegneria, Univ. Modena e Reggio E., 42100 Reggio E., Italy — ⁴School of Agric. Food and Biosys. Eng., Techn. Univ. Madrid, 28040 Madrid, Spain

Strong anomalous diffusion is often characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes ξ and ζ for small and large moments, respectively, and by the critical moment α of the crossover. Higher moments are asymptotically dominated by ballistic excursions; lower moments correspond to weak anomalous diffusion. We argue that ξ and ζ characterize the asymptotic scaling of the bulk and the tails of the distribution, respectively. Asymptotic theory is adopted to match the behaviors at intermediate scales. The resulting constraint entails that strong anomalous diffusion emerges if the distribution has algebraic tails, and it relates α to the corresponding power law. Our theory provides the leading-order corrections to the asymptotic power-law behavior. This insight allows us to point out sources of (at times) severe systematic errors in numerical estimates of the moments of displacement. Rather than fitting exponents we devise a robust scheme to determine ξ, ζ and α. The findings are supported by numerical and analytical results on different models exhibiting strong anomalous diffusion.