LIMIT BEHAVIOR OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS*

doi:10.1007/s10473-023-0123-6

摘要/Abstract

摘要： We study the ground states of attractive binary Bose-Einstein condensates with $N$ particles, which are trapped in the steep potential wells $\lambda V(x)$ in $\mathbb{R}^2$. We show that there exists a positive number $N_{*}$ such that if $N>N_{*}$, the system admits no ground state for any $\lambda>0$. Moreover, there exist two positive numbers, $M_{*}$ and $\lambda^*(N)$, such that if $N<M_{*}$, then for any $\lambda>\lambda^*(N)$, the system admits at least one ground state. As $\lambda\rightarrow\infty$, for any fixed $N<M_{*}$, we give a detailed description for the limit behavior of both positive and semi-trivial ground states.

关键词: ground state, binary Bose-Einstein condensate, steep potential well, limit behavior

Abstract: We study the ground states of attractive binary Bose-Einstein condensates with $N$ particles, which are trapped in the steep potential wells $\lambda V(x)$ in $\mathbb{R}^2$. We show that there exists a positive number $N_{*}$ such that if $N>N_{*}$, the system admits no ground state for any $\lambda>0$. Moreover, there exist two positive numbers, $M_{*}$ and $\lambda^*(N)$, such that if $N<M_{*}$, then for any $\lambda>\lambda^*(N)$, the system admits at least one ground state. As $\lambda\rightarrow\infty$, for any fixed $N<M_{*}$, we give a detailed description for the limit behavior of both positive and semi-trivial ground states.

Key words: ground state, binary Bose-Einstein condensate, steep potential well, limit behavior

Yuzhen kong, Zhiyuan cui, Dun zhao. LIMIT BEHAVIOR OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS^*[J]. 数学物理学报(英文版), 2023, 43(1): 409-438.

Yuzhen kong, Zhiyuan cui, Dun zhao. LIMIT BEHAVIOR OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS^*[J]. Acta mathematica scientia,Series B, 2023, 43(1): 409-438.

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LIMIT BEHAVIOR OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS^*

LIMIT BEHAVIOR OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS^*

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