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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We rigorously compute the integrable system for the limiting$(N\rightarrow\infty)$ distribution function of the extreme momentum of $N$noninteracting fermions when confined to an anharmonic trap $V(q)=q^{2n}$ for$n\in\mathbb{Z}_{\geq 1}$ at positive temperature. More precisely, the edgemomentum statistics in the harmonic trap $n=1$ are known to obey the weakasymmetric KPZ crossover law which is realized via the finite temperature Airykernel determinant or equivalently via a Painlev\'e-II integro-differentialtranscendent, cf. \cite{LW,ACQ}. For general $n\geq 2$, a novel higher orderfinite temperature Airy kernel has recently emerged in physics literature\cite{DMS} and we show that the corresponding edge law in momentum space is nowgoverned by a distinguished Painlev\'e-II integro-differential hierarchy. Ouranalysis is based on operator-valued Riemann-Hilbert techniques which produce aLax pair for an operator-valued Painlev\'e-II ODE system that naturally encodesthe aforementioned hierarchy. As byproduct, we establish a connection of theintegro-differential Painlev\'e-II hierarchy to a novel integro-differentialmKdV hierarchy.

Momenta spacing distributions in anharmonic oscillators and the higher order finite temperature Airy kernel