Axial Symmetry and Refined Spike Profiles of Ground States for Rotating Two-Component Bose Gases

Yongshuai Gao, Yong Luo

Yongshuai Gao, Yujin Guo, Yan Li +1 more

Yongshuai Gao, Luo, Yong

This paper considers ground states of two-component Bose gases confined in an anharmonic trap rotating at the velocity $0<Ω<\infty$, where the intraspecies interaction $(-a_1,-a_2)$ and the interspecies interaction $-β$ are both attractive, i.e, $a_1, a_2$ and $β$ are all positive. We prove the axially symmetry and the refined spike profiles of ground states as $β\nearrowβ^*:=a^*+\sqrt{(a^*-a_1)(a^*-a_2)}$, where $00$ is the unique positive solution of $-Δu+u-u^3=0$ in $\mathbb{R}^2$.

Yongshuai Gao, Yujin Guo, Yan Li +1 more

This paper is concerned with ground states of two-component Bose gases confined in a harmonic trap $V(x)=x_1^2+Λ^2 x_2^2$ rotating at the velocity $Ω>0$, where $Λ\ge 1$ and $(x_1, x_2)\in R^2$. We focus on the case where the intraspecies interaction $(-a_1,-a_2)$ and the interspecies interaction $-β$ are both attractive, i.e, $a_1, a_2$ and $β$ are all positive. It is shown that for any $0<Ω<Ω^*:=2$, ground states exist if and only if $00$ is the unique positive solution of $-Δw+ w-w^3=0$ in $R^2$. By developing the argument of refined expansions, we further prove the nonexistence of vortices for ground states as $β\nearrowβ^*$, where $0<Ω<Ω^*$ and $0

Elife Öznur Karabulut, Francesc Malet, G. M. Kavoulakis +1 more

Wenlei Li, Qinglin Tang, Jing Wang +2 more