Berlin 2018 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 60: Anomalous Diffusion (joint session DY/BP)

DY 60.2: Vortrag

Donnerstag, 15. März 2018, 10:15–10:30, BH-N 334

Anomalous Diffusion in Complex Dynamical Systems: Diffusing Diffusivity Models — •Rohit Jain and Kizhakeyil L Sebastian — Indian Institute of Science, Bangalore 560012, India

Diffusion inside a crowded, rearranging environment has attracted a lot of attention recently [1]. In such systems, the mean square displacement of diffusing particle remains Fickian obeying ⟨x²⟩∝ T, yet the distribution of displacements is not Gaussian. Following the work of Chubynsky and Slater [2], we have proposed a class of analytically solvable models where the diffusion coefficient becomes a random function of time [3]. The results obtained with our model are in very good agreement with the simulations of Chubynsky and Slater (see also [4]).

In a different model [5], we have analyzed a case where diffusivity evolves as a Lévy flight process. That is, the distribution of diffusivity decays as power-law of the form D^−1−α with 0 < α < 1, for large D. The distribution of displacements with this model is found to be a Lévy stable distribution with a time dependent width. With this model, the dynamics is Brownian at short times and superdiffusive at long times.
References:
[1] Wang et. al., Proc. Natl. Acad. Sci. U.S.A., 106, 15160 (2009).
[2] Chubynsky and Slater, Phys. Rev. Lett. 113, 098302 (2014).
[3] Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016).
[4] Chechkin et. al., Phys. Rev. X 7, 021002 (2017).
[5] Jain and Sebastian, Phys. Rev. E 95, 032135 (2017).