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 study the mean-field and semiclassical limit of the quantum many-bodydynamics with a repulsive $\delta$-type potential $N^{3\beta}V(N^{\beta}x)$ anda Coulomb potential, which leads to a macroscopic fluid equation, theEuler-Poisson equation with pressure. We prove quantitative strong convergenceof the quantum mass and momentum densities up to the first blow up time of thelimiting equation. The main ingredient is a functional inequality on the$\delta$-type potential for the almost optimal case $\beta\in(0,1)$, for whichwe give an analysis of the singular correlation structure between particles.

On the mean-field and semiclassical limit from quantum $N$-body dynamics