Axial Symmetry and Refined Spike Profiles of Ground States for Rotating Two-Component Bose Gases
arxiv(2023)
摘要
This paper considers ground states of two-component Bose gases confined in an
anharmonic trap rotating at the velocity $0<\Omega<\infty$, where the
intraspecies interaction $(-a_1,-a_2)$ and the interspecies interaction
$-\beta$ are both attractive, i.e, $a_1, a_2$ and $\beta$ are all positive. We
prove the axially symmetry and the refined spike profiles of ground states as
$\beta\nearrow\beta^*:=a^*+\sqrt{(a^*-a_1)(a^*-a_2)}$, where $00$ is the unique positive solution of
$-\Delta u+u-u^3=0$ in $\mathbb{R}^2$.
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