TY  - GEN
A1  - Ślęzak, Jakub
A1  - Metzler, Ralf
A1  - Magdziarz, Marcin
T1  - Superstatistical generalised Langevin equation
BT  - non-Gaussian viscoelastic anomalous diffusion
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 413 
KW  - anomalous diffusion
KW  - generalised langevin equation
KW  - superstatistics
KW  - non-Gaussian diffusion
Y1  - 2018
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-409315
ER  - 
TY  - JOUR
A1  - Ślęzak, Jakub
A1  - Metzler, Ralf
A1  - Magdziarz, Marcin
T1  - Superstatistical generalised Langevin equation
BT  - non-Gaussian viscoelastic anomalous diffusion
JF  - New Journal of Physics
N2  - 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.
KW  - anomalous diffusion
KW  - generalised langevin equation
KW  - superstatistics
KW  - non-Gaussian diffusion
Y1  - 2018
U6  - https://doi.org/10.1088/1367-2630/aaa3d4
SN  - 1367-2630
VL  - 20
IS  - 023026
SP  - 1
EP  - 25
PB  - Deutsche Physikalische Gesellschaft / Institute of Physics
CY  - Bad Honnef und London
ER  -