New Journal of Physics
New Journal of Physics
5 years ago

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We s...

Publisher URL: http://iopscience.iop.org/1367-2630/20/2/023026

DOI: 10.1088/1367-2630/aaa3d4

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