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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Analytically tractable dynamical systems exhibiting a whole range of normaland anomalous deterministic diffusion are rare. Here we introduce a simplenon-chaotic model in terms of an interval exchange transformation suitablylifted onto the whole real line which preserves distances except at a countableset of points. This property, which leads to vanishing Lyapunov exponents, isdesigned to mimic diffusion in non-chaotic polygonal billiards that give riseto normal and anomalous diffusion in a fully deterministic setting. As thesebilliards are typically too complicated to be analyzed from first principles,simplified models are needed to identify the minimal ingredients generating thedifferent transport regimes. For our model, which we call the slicer map, wecalculate all its moments in position analytically under variation of a singlecontrol parameter. We show that the slicer map exhibits a transition fromsubdiffusion over normal diffusion to superdiffusion under parameter variation.Our results may help to understand the delicate parameter dependence of thetype of diffusion generated by polygonal billiards. We argue that in differentparameter regions the transport properties of our simple model match todifferent classes of known stochastic processes. This may shed light ondifficulties to match diffusion in polygonal billiards to a single anomalousstochastic process.

A simple non-chaotic map generating subdiffusive, diffusive and superdiffusive dynamics