TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Ageing and confinement in non-ergodic heterogeneous diffusion processes
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We study the effects of ageing-the time delay between initiation of the physical process at t = 0 and start of observation at some time t(a) > 0-and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, D(x) = D-0 vertical bar x vertical bar(alpha). From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement.
KW  - stochastic processes
KW  - anomalous diffusion
KW  - ageing
KW  - weak ergodicity breaking
Y1  - 2014
U6  - https://doi.org/10.1088/1751-8113/47/48/485002
SN  - 1751-8113
SN  - 1751-8121
VL  - 47
IS  - 48
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Sanders, Lloyd P.
A1  - Lomholt, Michael A.
A1  - Lizana, Ludvig
A1  - Fogelmark, Karl
A1  - Metzler, Ralf
A1  - Ambjoernsson, Tobias
T1  - Severe slowing-down and universality of the dynamics in disordered interacting many-body systems: ageing and ultraslow diffusion
JF  - New journal of physics : the open-access journal for physics
N2  - Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form < x(2)(t)> similar or equal to t(alpha) of the mean squared displacement with 0 < alpha < 1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics < x(2)(t)> similar or equal to log(1/2)t with a universal 1/2 exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement < x(2)(t)> similar or equal to t(gamma) with 0 < gamma < 1/2, that is slower than the famed Harris law < x(2)(t)> similar or equal to t(1/2) without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process.
KW  - single-file diffusion
KW  - continuous time random walks
KW  - ageing
Y1  - 2014
U6  - https://doi.org/10.1088/1367-2630/16/11/113050
SN  - 1367-2630
VL  - 16
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -