English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

As well known, the generalized Langevin equation with a memory kerneldecreasing at large times as an inverse power law of time describes the motionof an anomalously diffusing particle. Here, we focus attention on some newaspects of the dynamics, successively considering the memory kernel, theparticle's mean velocity, and the scattering function. All these quantities arestudied from a unique angle, namely, the discussion of the possible existenceof a distribution of relaxation times characterizing their time decay. Althougha very popular concept, a relaxation time distribution cannot be associatedwith any time-decreasing quantity (from a mathematical point of view, the decayhas to be described by a completely monotonic function). Technically, we use amemory kernel decaying as a Mittag-Leffler function (the Mittag-Lefflerfunctions interpolate between stretched or compressed exponential behaviour atshort times and inverse power law behaviour at large times). We show that, inthe case of a subdiffusive motion, relaxation time distributions can be definedfor the memory kernel and for the scattering function, but not for theparticle's mean velocity. The situation is opposite in the superdiffusive case.

Relaxation time distributions for an anomalously diffusing particle