@misc{ŚlęzakMetzlerMagdziarz2018,
  author    = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin},
  title     = {Superstatistical generalised Langevin equation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-409315},
  pages     = {25},
  year      = {2018},
  abstract  = {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 show that our theoretical results are in excellent agreement with stochastic simulations.},
  language  = {en}
}