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 prove the existence of smooth solutions to the Gross-Pitaevskii equationon $\mathbf{R}^3$ that feature arbitrarily complex quantum vortexreconnections. We can track the evolution of the vortices during the wholeprocess. This permits to describe the reconnection events in detail and verifythat this scenario exhibits the properties observed in experiments andnumerics, such as the $t^{1/2}$ and change of parity laws. We are mostlyinterested in solutions tending to1 at infinity, which have finiteGinzburg-Landau energy and physically correspond to the presence of abackground chemical potential, but we also consider the cases of Schwartzinitial data and of the Gross-Pitaevskii equation on the torus. An essentialingredient in the proofs is the development of novel global approximationtheorems for the Schr\"odinger equation on $\mathbf{R}^n$. Specifically, weprove a qualitative approximation result that applies for solutions defined onvery general spacetime sets and also a quantitative result for solutions onproduct sets in spacetime $D \times \mathbf{R}$. This hinges onfrequency-dependent estimates for the Helmholtz-Yukawa equation that are ofindependent interest.

Approximation theorems for the Schr\"odinger equation and quantum vortex reconnection