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

We explore wave-mechanical scattering in two spatial dimensions assuming thatthe corresponding potential is invariant under linear symmetry transforms suchas rotations, reflections and coordinate exchange. Usually the asymptoticscattering conditions do not respect the symmetries of the potential and thereis no systematic way to predetermine their imprint on the scattered wave field.Here we show that symmetry induced, non-local, divergence-free currents can bea useful tool for the description of the consequences of symmetries on higherdimensional wave scattering, focusing on the two-dimensional case. Thecondition of a vanishing divergence of these non-local currents, being inone-to-one correspondence with the presence of a symmetry in the scatteringpotential, provides a systematic pathway to to take account if the symmetriesin the scattering solution. It leads to a description of the scattering processwhich is valid in the entire space including the near field regime.Furthermore, we argue that the usual asymptotic representation of thescattering wave function does not account for insufficient account for a properdescription of the underlying potential symmetries. Within our approach wederive symmetry induced conditions for the coefficients in the wave fieldexpansion with respect to the angular momentum basis in two dimensions, whichdetermine the transition probabilities between different angular momentumstates.

Non-local divergence-free currents for the account of symmetries in two-dimensional wave scattering